In that case use your company provided account. Just like all tools I would expect that to be provided by the company and as such availability of these tools wouldn't be my problem.

Also, use a private account for private stuff, if that wasn't obvious

That’s between you and your boss, and likely your GitHub account rep. It’s still not a monopoly just because someone voluntarily chooses not to use alternatives.

Create a new GitHub account that you use for work.