My experience is a bit different from yours, so I wonder if there is something specific to your environment that is contributing to or causing this.
1. I use Enpass on a few Macs, Intel and Apple Silicon with either Monterey or Ventura and I’ve not experienced this. When the machine wakes from sleep, Enpass is still responsive.
2. I don’t use stage manager, but I just tried it and it seemed ok, but I can’t really comment on this because one data point doesn’t mean there isn’t an issue, look around the forum and see if anyone else is complaining of this.
3. I also don’t use a separate key any more, so I can’t test this.
4. I regularly use Safari and Firefox enough to say that this doesn’t seem to be a broad issue. So long as Enpass is running and linked properly to the browser extension and you are using the latest version of that extension, I’ve not had a problem with Enpass triggering. I can’t comment on Chrome, since while I do have it installed and the extension active, I don’t use it enough to say for sure that there isn’t an issue.
5. I’ve never had the Safari extension crash on any of my Macs. Honestly, I’ve never had any Safari extension crash on me, but I also don’t have a bunch active.
All this makes me wonder if there is something specific to your environment that is causing most of this. For example some interaction with other software you have installed or some cruft or something else damaged that is making Enpass unstable. If the issues you report were widespread, there would be a lot of similar reports here, since you are basically saying Enpass is unusable, and that would definitely get people (me too) here to complain about the problem.
Assuming you want to continue to use Enpass, there are a few things you can do to try to narrow down the problems you are having.
The best way is to either backup your boot drive and wipe it and reinstall macOS or copy your vault over to a new Mac before anything else is installed or configured and see if the problems go away.
I particularly think that backing up regularly and wiping your drive (or using macOS’s built-in data removal and os reconfiguring feature) periodically can really help. (I do the wipe and start fresh thing every year or so, and I find it really helps on Macs and PCs.)
To be more specific, get an external hard drive and back up all of your data. I like using something like Carbon Copy Cloner or Super Duper to create a “bootable” backup so I can be sure that all of my data is intact. (For security, Apple makes it really hard to boot from external sources on modern Macs.) Once you have a good backup (with really important data backed up in multiple ways to be safe), restart your Mac in recovery mode, wipe the boot drive and reinstall the OS.
You can also erase the Mac, but I prefer the wipe and reinstall method to be sure.
Once the OS is reinstalled, the first thing to do is to install Enpass, since that is the app you’re having problems with, copy over your vaults as well. Then activate Enpass if needed and test all of the things you had issues with. If the problems don’t go away, try one more thing. Remove the vaults and create a brand new one. Add a few logins to the vault for testing and then try everything again. If the problems go away, you know that there was something with your old setup or the vaults themselves causing the problem.
If it is your old vaults, try exporting the data from them and importing only the data you really need into the new vault and if the problem(s) return, there might be some bad or corrupted entries in the vault causing problems.
Chances are, based on the issues you report, that bad vault entries are unlikely to be the cause of all of the problems. If wiping and reinstalling solves the problems, you still aren’t done, because you might as well check that some other software you need isn’t reacting with Enpass to cause problems. In this case, only reinstall your most critical software items one at a time, testing Enpass for issues after each install. If the problems don’t return, great! If they do, note what you installed before the issue reappeared and report the conflict to both developers since the issue might be on both sides.
Not related to this, but I find it super useful… If you do this, only reinstall software you know you must use immediately (perhaps an VPN for work, or software you know you use every day) and hold off on reinstalling everything you had previously installed. If you then run into an issue where you realize you need the software that isn’t installed, reinstall it at that point. Especially if you’ve been using your Mac for a while you definitely have things installed you likely no longer use, and this is a chance to free up disk space and simplify your life by not installing stuff you don’t need.
I hope this helps.