Can my employer see my phone browsing history on my work desktop?

What if i logged in my work pc using my personal google account?

Can my employer see what i have been googling on my phone under my work desktop’s browsing history?

What about under “my activity” in google? Would it be auto synced? (simply put – i logged in my work pc + personal mobile using the same Google account.. So would my private searches done using my phone be available on my work pc?)