I ran through the rabbit hole of trying to get the newest rstudio to work with the new version of ubuntu. When it says that the libssl is uninstallable, you will find a bunch of threads giving links to fix it but they don't fix it anymore because those links don't exist anymore.
Solution: Follow http://http.us.debian.org/debian/pool/main/o/openssl/ and look for the libssl that is going to work for you. The one I used, current to end of May 2022, is libssl1.1_1.1.1n-0+deb10u1_amd64.deb
When you run the code with the new found package, it will work:
wget 'http://http.us.debian.org/debian/pool/main/o/openssl/libssl1.1_1.1.1n-0+deb10u1_amd64.deb'
sudo apt-get install ./libssl1.1_1.1.1n-0+deb10u1_amd64.deb
sudo apt-get install ./rstudio-2022.02.2-485-amd64.deb
rstudio --no-sandbox
This code will need updated in the future, follow my instructions above to do so if you are looking at this at a later date. You will need to find the new version of libssl1.1_1.1.1n-0+deb10u1_amd64.deb and replace it.
Correction: I didn't install the newest version of Rstudio, read through the above comments and noticed there are newer versions.