Some cranksets are modular. I'm not sure if this is a standard term, but I do mean that the crankarms fit to the spider with a splined interface. Thus, you can replace the spider. Less commonly, on some modular cranks, you can even replace the spindle for a different type, but that's not relevant here (I am thinking Rotor cranks; Quarq isn't this type of modular). Shimano's road cranksets are not modular at all - the crank arms and spider are forged together, and the spindle is bonded in (i.e. industrial strength glue). They can't be separated without destroying the crank.
And now, we come to power meters. Stages popularized a setup where they bonded strain gauges to the crank arms. This can be retrofitted to Shimano cranks, and probably most cranks (in principle, probably even SRAM cranks if there was actually market demand for this). I believe SRM, the original portable power meter, located its strain gauges more in the crank spider than on the arms. Quarq's strain gauges are definitely in the crank spider. So, if it must be a Quarq, you are replacing at least the crank arms, spider, and bottom bracket.
I realize this is complicated, but there are two things to consider with a bottom bracket. One is the bike's BB shell type. Yours is simple, it's a BSA threaded BB, a very common design. The other is the spindle size that the BB is designed to accommodate. This is where your problem lies. Shimano uses a 24mm spindle, so your bike came with a BB for that. SRAM uses the DUB standard, built around a 28.99mm spindle. You cannot cram that into the Shimano BB on your bike, it would not physically fit, and you'd destroy the bearings if it somehow fit and could actually turn.
More on the BB - not to nitpick, but while you do need a BSA DUB BB, you don't have to get it from SRAM if you don't want to. There are third party manufacturers who make this standard. By third party, I mean that Shimano is not one of those manufacturers. I'm using that in a similar sense to the word aftermarket.
An earlier version of this answer said you needed to get a model called the DFour91 to be able to reuse your stock Shimano rings, otherwise you'd have to get a set of 5-bolt, 110mm BCD rings. I was wrong. Quarq (which is owned by SRAM) now uses "DFour" to mean a spider compatible with Shimano's 4-arm 110mm BCD rings. There used to be a DFour91 model, which I got confused with. The DZero model is the one that takes 5-bolt 110mm BCD rings. Both models do use the same splined interface. I would get the DFour over the DZero if I were the OP since they are converting a Shimano bike with a road group (and indeed, I have one, but see the note on chainline).
To my knowledge, SRAM offers a set of carbon arms branded to Quarq. I'm not sure if the construction is comparable to their Red or to their Force carbon arms. Personally, I have a pair, and they look fine. Subjectively, the quality of the finish is decent, in the same range as Ultegra, maybe a bit less nice, but whatever. If you are getting a Quarq spindle, I believe it has to go with SRAM or Quarq crankarms - the splined interface should be the same. If I'm correct, then, you could bolt Force or Red crank arms to the bike if you wanted to, for some reason.
One last thing to consider is the crank's chainline. I believe you actually have a Diverge with GRX 810. (There is an RX800 rear derailleur with a clutch, but I believe that's the only component prefixed with RX, so there's no Shimano RX 810 anything. There doesn't appear to be a Diverge equipped with Ultegra; to be honest, the GRX gear ratios are generally much better for gravel bikes.) GRX 810 is an Ultegra-level set of components, but it has some different specifications. Specifically, its chainline is offset 2.5mm outwards to increase clearance. If you get a road DFour, you won't have the correct chainline. I think it would physically shift, and it may even shift well on at least some bikes, but it's not technically compatible and it is not guaranteed to shift well. I would recommend a crankset with the correct chainline. I am not very familiar with SRAM's offerings, but I believe that the GRX double cranks have a 46.9mm chainline, and Ultegra uses a 43.5mm chainline. SRAM's Rival Wide crankset (wide for wider gearing, I think this option is also available for Force) has a specified 47.5mm chainline, which should work. I am not sure if there's a Quarq-branded equivalent, or if all Quarq cranksets use the road double chainline - Quarq is definitely favored by triathletes and I don't think it's as widely used in gravel, so SRAM may not have created a Quarq crankset with a gravel bike-like chainline.
There are other power meter options available. You could get a Stages, 4iiii, or similar left arm with a power meter. That is left-only power. There's a chance that if you have other setups that measure total power (e.g. your road bike has a two sided meter, or you are comparing to a smart trainer), your numbers may not match exactly, but this may be something you can live with. You may even be able to ask either of the meters' firmware to offset your power (e.g. reduce it by a fixed percentage when reporting to the head unit, you'd do a functional threshold power test and concurrently record on, say, a smart trainer and your left arm powermeter, then determine how much you need to offset). I would mention Garmin's Vector pedals, but I realize now that they're pricier than a full DFour91 DUB setup would be (including BB and installation). Other SPD-compatible pedals comparable in price to the Quarq may yet come to market, however. And the OP noted in comments that Power2max has a power meter crankset + spider that uses the GRX chainline; I'd forgotten about them because I am in the US and they're not as common here (but they have branches in the US and many EU countries). I recall that their spiders have the options to take Shimano's 4-bolt road 110mm rings, Shimano's 4-bolt GRX rings (I don't recall the BCD), or 110mm, 5-bolt rings.
In the unlikely event you are looking at a closeout DFour with a 30mm spindle, note this thread on Slowtwitch.com. Some DFours may have had an issue where if you dropped your chain to the inside, it would hit the meter in such a way as to damage one of the strain gauges. This would render the meter inoperable. Dropped chains do sometimes happen on gravel, even with a properly adjusted setup. I am actually one of the victims. SRAM did replace the cranks that were within the warranty period and corrected the issue in manufacturing. Notwithstanding that, I'd be more hesitant about BB30 DFours, because I don't know which production lots were affected by this, and you don't know that if it breaks, it will do so within the warranty period. I can, at least, report that I similarly dropped my chain on the replacement DFour DUB, and it continues to function normally (and FWIW, my front derailleur hangar had come loose, unbeknownst to me, which caused the drops).
Last, a side note for readers not familiar with why I am conflating SRAM and Quarq: Quarq was a standalone power meter company. SRAM bought them some time ago, probably early to mid 2010s. SRAM is integrating Quarq into their lineup, but Quarq does still offer power meters and crankarms under its own branding; some Shimano users clearly opt for them, for example.