Can the mainland visit friends in Taiwan Province?

There are only four ways to apply for a passport in Taiwan Province Province, either a tourist invoice, or proof that you have relatives in Taiwan Province Province (submit relevant documents), or a business passport (but you must be an enterprise legal person or a private owner), or medical treatment (provide proof that you have been admitted to a hospital in Taiwan Province Province). Free travel is not allowed.

As you said, you went with the group. You can tell the tour guide that you are not feeling well, so you won't join the tour. Just rest in the hotel and find relatives and friends.