Most third party applications that I use are compatible. Much of my time is spent on MS Word, which just received an M1 compatibility update.
I unfortunately do not have an external SSD. I do have an external HDD, however. I suspect installing 11.1 on HDD might not be an effective way around.
I have installed V11.1 on my MBP E'2015, which seems to be working fine if you don't consider the issues that come with upgrading old Macs.
I have read some posts where people have complained about some issues brought on by V11.1. Although almost all of them sound non-issues for me. I might wait couple of days or so and see if Apple has any plan to further patch the upgrade. I have a base model M1 with 256GB and all these upgrades are slowly eating up my precious infinite SSD space that may be useful for other stuff.
That's good that most of the third party applications you use are compatible. I have two that are not, and thus why I am just testing Big Sur on my external SSD. I use LibreOffice for my word processing and spreadsheet needs, and it works fine (can read a write numerous Word and Excel formats).
You did not say if you are making backups to an external device. That is just about a necessity.
While using that external HDD might not be ideal, there would be nothing wrong in using it for testing Big Sur. It will be somewhat slow to boot to, and possibly running applications (especially if it is a 5400 rpm HDD).
I have said all along that even when V11.1 is released, there will still be bugs. Well, sure enough, yesterday a new beta version V11.2 of Big Sur arrived:
Apple today seeded the first beta of an upcoming macOS Big Sur 11.2 update to developers for testing purposes, with the new beta coming two days...
www.macrumors.com
So, looks like V11.1 still has some issues, although I am not seeing any (at least ones that are serious. I am seeing two very minor ones, though). V11.1 has actually been rather solid for me.