I understand private keys being compromised is a huge risk; however, what about public keys. If someone were to access my public key associated with the private key I use to SSH in the Linux server, and modify it, wouldn’t that prevent me access to the server; therefor, affecting availability on my end?

You can always regenerate a public key as long as you have the private key.

You ask:

If someone were to access my public key associated with the private key I use to SSH in the Linux server, and modify it, wouldn’t that prevent me access to the server; therefor, affecting availability on my end?

So is the situation you are concerned about something like you leave your computer on, don’t put it to sleep, run away to do something, then someone goes to your computer and just adds a few characters to your public key so it is effectively damaged? Or even deletes it?

No worries as long as you have your private key. Just run this command:

ssh-keygen -y -f ~/.ssh/id_rsa > ~/.ssh/id_rsa.pub

And your public key will be regenerated. Just note that the comment at the end of the public key line that allows you to more easily identify which key is what—via what is typically an email address—won’t be added to this id_rsa.pub via this method. So you might want to open it up in a text editor and manually add that.

About your other concerns.

Now if you are concerned about someone hacking the public key on a remote machine in a way that denies you access? Honestly, you would have a fairly larger issue to deal with in a case like that.

Typically, someone would need to be able to gain root access on a machine to do that. And that is not unheard of but a rare occurrence at best.

The whole point of a public key is to be widely known. It can be vetted by the PKI (public key infrastructure). You can sign messages (and other things) with your private key locally on your PC, and others can confirm that the message came from you.

Similarly, the public key can be put into the SSH config files on remote servers. When you SSH into those servers, they present a challenge that can only be correctly answered by someone with the proper private key.

Your original question asked:

"If someone were to access my public key associated with the private key I use to SSH in the Linux server, and modify it"...

then it would no longer be the same public key. You can regenerate the public key immediately for another admin to set the proper public key.

You have secondary worries: Who else can get access to my machine, what can they do, and how do I recover? hose answers are complicated and situational.

There are many good resources on SSH and PKI on the web... here's a good start: SSH Essentials: Working with SSH Servers, Clients, and Keys