What to check as a solo booker
Whether the departure is confirmed or still needs a minimum number of participants.
Accommodation: mountain huts are shared dormitories with no supplement; inn-to-inn trips often have a single-room supplement.
The stated fitness level, so the group moves at a pace you will enjoy.
Private versus joining a group
A private guide gives you the route and pace you want at the full day rate. Joining an existing small group splits that cost and is usually the better value, at the price of some flexibility.
Related questions
Are guided groups mostly couples?
Mixed, and solo participants are normal on every departure. Guides plan for it.