Tempered glass does not work well, or work like it does not have a protector on it for the S21reg like it should. The glass is typicaly not near as accurate, gave me alot of "no match" and I had to try again, sometimes multiple times. It also slowed down the opening of the phone for me. I also found I had to press harder and longer. I have tried many different protectors, glass and film, and the one that works and feels the best for me is the amFilm hybrid. I have always only used glass in the past, but they just don't make one yet that works as well as it should with the S21reg. The AmFilm Hybrid feels alot like glass and the fingerprint scanner works flawlessly. Very happy with this product. https://www.amazon.com/dp/B08RYV6PD5/ref=cm_sw_r_sm_apa_fabc_XS6BAQTTZR98F421HNAV
As long as they are not glass, there are a couple of expensive glass ones that work great e.g. Whitestone Dome. If you removed the factory screen protector, which is a very thin film for scratch protection. There are non glass screen protectors that allow the best fingerprint scanner made work flawlessly. My non glass suggestion would be the amFilm HD Clear Hybrid (2 Pack) https://www.amazon.com/dp/B08RYV6PD5/ref=cm_sw_r_apan_glt_fabc_3YQRV3SP142Y3V3C8G8N
I have used this one myself and it works as good as if there was no screen protector on at all, just simply apply, re-register your prints, turn on the screen sensitivity toggle and you should be 100% satisfied, but other people may have other suggestions. Good luck.
I did the same thing with another brand AMOVO and it was the same crappy performance you had. There is a post here that says the AmFilm Hybrid works perfectly and feels exactly like glass. I sent back my AMOVO and ordered the amFilm Hybrid.
https://www.amazon.com/dp/B08RYV6PD5/ref=cm_sw_r_sm_apa_fabc_PT5790CGFMJ3ZTMXNTKC
https://www.reddit.com/r/GalaxyS21/comments/l78qx7/s21_screen_protectors_tested_what_works_and_what/
Someone suggested this: https://smile.amazon.com/amFilm-Protector-Fingerprint-Compatible-Installation/dp/B08RYV6PD5
and I might go with it
This links to the S21 rather than S21+ but I am sure they sell for both: https://www.amazon.com/gp/product/B08RYV6PD5/ref=ppx_yo_dt_b_asin_title_o02_s00?ie=UTF8&psc=1. Amfilm is not only cheaper than Zagg, the fit is better, it is more fingerprint resistant, and the screen feels less like plastic. The fingerprint sensor also has a much lower failure rate than with the Zagg it replaced. It took about two minutes to install as well....