On my work computer, I have connected to my personal Gmail account to check my email and go to my drive. At home I use my own personal phone and/or laptop.
Can my employer see what I'm searching and looking at through my phone (never connected to their network) or computer (using my own WiFi), since my Gmail is connected to my work computer?
If you connected to your Google account on your work computer, your employer may know your login credentials. Your employer may employ a TLS proxy, which allows them to inspect TLS secured traffic (e.g. HTTPS traffic). If this is the case, they could also see the contents of emails as they are transferred from Google's servers to your work computer.
However, that does not mean that your employer would actually do that. I'm not a lawyer, so please don't expect legal advice from me, but it is common for employees to sign various policies, especially regarding to what is monitored on their work computer.
In general, you have to expect that an employer can see everything you do on their computer. That doesn't mean they actually do look, just that they can.
As for reading your emails when you are on your home PC, your employer can not read those, even if you have connected to that account previously on your work PC. Theoretically, an employer who knows your credentials can attempt to log into your Gmail account, although that would most likely be illegal in most jurisdictions, and get them in deep trouble. Furthermore, you will likely get a security alert if a new unknown device attempts to log into your Gmail account.
In order to ensure the security of your account, I would advise you not to check your private emails on your work computer and to set up 2FA authentication.
