Are you sure?
Note, that the filename is the same for Ubuntu 22:
https://download1.rstudio.org/desktop/jammy/amd64/rstudio-2022.07.2-576-amd64.deb
The download URL differs, note the ābionicā in my link, and ājammyā here.
The .deb packages are different. Based just on the filename itās impossible to tell which version you really downloaded. Also checking the hash would tell surely, which you have, the filesize gives a hint too.
But no problem if Iām wrong, itās not unusal 
But get back your problem.
There are some practices, youprobably donāt know yet.
If you did not use a filesystem encryption, accessing your data on your damaged Linux installation is fairly easy.
First, boot up live USB!
You will get a fully working environment, youāll be able to mount partitions, disks on your system. You can use the filemanager of the liveUSB to mount any partition on your computer, be it on the on the built-in SSD/HDD, or on a just attached external HDD.
Just browse the contents of the folders, do copy/paste (preferably from source to destination
).
Your data you might want to backup is stored in your home folder. Thatās something like /home/your_username/, so look for a derictory called your_username under a āhomeā diretory.
So backing up your data is not more difficult, than copy files and dirs from a disk to another. Just substitute your_username with your actual login name on your installed system.
Maybe this video shows some of the basic ideas
Regarding making your system bootable, as I mentioned, Iād chroot into it.
Now I try to give some hints to that:
you have your liveUSB booted up.
If you mounted some partitions, disks using the filemanager, unmount them.
Start a terminal (ctrl-alt-T usually does this).
Get root, to avoid to having to type too many āsudoā commands, Iām awfully lazy, so I always do this. So in the terminal:
sudo su
I assume, you already know whereās your system installed. I mean disk and partition. For the simplicity letās say itās sda1. Itās the first partition of the sda disk.
I would mount it to /mnt, so in the terminal:
mount /dev/sda1 /mnt
So if you know cd to /mnt, youāll see the contents of your system partitions.
If you have it on a different disk or partition, substitute /dev/sda1 with your actual values.
Iād try to chroot into that installed system, that basically means, any commands do things on the installed system, changes made via apt remove affect that installed system. So in the terminal:
chroot /mnt
Youāll get a root shell, and whatever you now, you do it with your installed system.
Iād try to remove rstudio packages:
apt purge rstudio*
apt autoremove --purge
Both commands will ask you for a confirmation wether you really want to remove those packages.
Exit from chroot, unmount your partition and reboot:
exit
umount /mnt
reboot
See, if your system works?