Since you already know about limit screws and derailleur hangers, you probably checked this first, but are you sure it's not just a case of needing a bit more cable tension on that derailleur? I.e. backing out one of the inline barrel adjusters on that derailleur's cable a half turn or so.
Keeping pressure on the shift lever like you mentioned simulates a little extra cable tension, and the fact that it will actually get to that gear suggests that the limit screw is not grossly out of range. You also mention it's a new-ish bike, and cable stretch in the first few weeks or months with a new bike, leading to exactly this type of degradation in shifting in that time frame, is a common scenario and usually fixed by simply adding a little cable tension.
Tiny adjustments are key. One approach I find works well is put the bike in a workstand, or hang it with some rope, or even just have another person hold the rear wheel off the ground. Then, without pedaling, shift into the gear you're having trouble with. Then start turning the pedals slowly. You'll then probably observe the chain do one of a few things:
- Shifts to the target gear but then makes clicky noises and occasionally drops back to the smaller cog and/or moves back and forth spontaneously. The cable needs a tiny bit more tension in this case. You may find 1/8 to 1/2 turn sufficient to fix this.
- Doesn't fully shift to target gear but gets part way there, e.g. rides up onto the larger cog for part of a cassette revolution before dropping back down. Will need more tension than the above case.
- Doesn't shift or ride up but start making clicky sounds. Needs even more tension than previous case.
- Doesn't shift or make any clicking sounds. Needs a lot of cable tension added.
If you find you have to back a barrel adjuster way out, you may instead want to wind it all the way in, and then unclamp the cable at the derailleur and pull in a larger amount of slack there before continuing with fine adjustment at the barrels. Ideally you don't want those spooled all the way out to the point where there's no room left for a mid-ride tension increase. And obviously you don't want them popping right out of their threads.
After the above, when you find the cable tension setting that makes the gear shift cleanly in a workstand setting, sometimes you'll need to then spool it back in a tiny amount (remove a bit of tension) to factor in that when you're shifting during a ride, you usually provide a little tension boost during the shift before releasing the shifter.
Finally, as mentioned in the comments below, you may find after working cable tension back and forth that you can't get a single tension setting that makes your derailleur work well across the entire cassette. E.g. maybe you can get it indexed really well for the 4 largest cogs, but then the 4 smallest cogs don't shift well. Then you fiddle it the other way and now the 4 smallest cogs shift great and the 4 largest are bad. And there's no way to get all of them shifting well. That's a hint that there's something else wrong besides cable tension. Could be a bent hanger as mentioned. I've also had the same thing happen when I had a very worn chain + casette (probably not the case here given the age of your bike). I've also had similar happen when I had a defective cable where the steel cable wrap had loosened bit over about an inch of cable that happened to sit right under the bottom bracket. So that caused extra friction and crummy shifting in a couple of gears as that portion of cable passed under the BB.