The things your story leaves unclear: if the rear didn't have any bleed type symptoms when you first brought it, why did it get bled at any point? Bleeding doesn't usually happen preventitively in shops and also not as part of a pad replacement. Unless they did it preventitively as part of some kind of service package and then did a bad job of it, it's curious what happened to the brake that made it need it in the first place. It's also curious what happened to make it lose the pad, which is highly unusual. It is possible to make the mistake of not getting a pad retaining pin properly through a brake pad, and that's one way of losing them, and it's also possible for the pad material to come separate from the backplate, but that's rare. (I have seen it once on a new Covid-era brake pad on a new bike, of hundreds I see a year, and never before the past year). So all told, it's really unclear what happened to this brake and why. It's possible that what happened is when the pad came off, the piston behind it got overextended to the point of leaking fluid or coming out completely, which would then require a bleed. That chain of events makes sense but the extreme weirdness of losing a pad like that still makes it feel like there could be something more going on.
As to the question, the answer is that when the quality of the bleed is good on both brakes and there's still a mismatch in feel and/or travel, the options are limited and mostly involve going a lot more in-depth to even try.
For travel aka bite point, first note that almost all hydro levers have reach adjust, but that's not relevant because it has little or no bearing on bite point, just reach, and any effect it does have on bite point isn't relevant because if you use it that way you're making the starting reach of the brakes asymmetrical. Some levers do have bite point adjustment that's independent of the reach adjust, which in some situations can be used to make lever feel more symmetrical, but even then usually only when something is wrong with one of the brakes that's bringing its bite point artificially far out, like over-extended pads that result from sticky pistons. So making the bite point adjustment asymmetrical can be a piece of the puzzle in tuning feel when you have bite point adjustment, but mostly only when something else is wrong.
Other than the above, there is basically no tuning bite point. It tends to be at its furthest out with new pads, although how much difference that makes depends on the specific brake and whether it's an open or closed system etc. Sometimes people mess around with intentionally overextending the pistons during a bleed (intentional fluid overfill) to get a shorter bite point, but most of the time that's a bad idea because it makes the pad gap less than it should be. It's anything but a normal thing to do.
For feel, it is true that all rear brakes feel squishier than their matching fronts even when things are perfect. What makes a brake feel firm is no air, no compression of the fluid, and no flexing of the hose. No fluid or hose is perfect, and rears have more of both, hence more squishy feel. It is a relatively minor effect but it's always there, unless maybe you do something drastic and weird like mismatch hose types. This effect is princess-and-the-pea level, and tiny compared to soft feel that results from air contamination in the line, which makes the brake feel like mush.
There is no using the bleed procedure to tune the feel, other than the aforementioned intentional fluid overfill hacks, which can be done by using a shaved bleed block etc. Bleeding takes all the air out and is successful when it does that and unsuccessful if not.
Piston stickiness can cause pad retraction issues that reduce the pad gap and also reduce lever stroke, but not feel mushy. Those issues are not always possible or cost-effective to fix; it's pretty common for a new caliper to be the only practical way, and so they are responsible for shops doing everything possible in some situations and still handing back a bike with significantly asymmetrical brake feel, but neither brakes should still be mushy. There are a lot of brakes where it's common to have some level of this even though the brake is still functional - many Avid/SRAM models are like that.
