Welcome to the affliction - make room for more.
Indeed an early first year rifle - 2266 made in 1906! Many here take the rifle down before shooting (not a bad thing for sure). Others of us check for function, as you have done, then go out and shoot it.

The good news, rarely is the barrel spring an issue - even rusted with crud around it! (Plus it is a bit of a pain to remove!) IMHO if it functions and you can manually make it completely recoil and the exposed part of the barrel looks good, I'd shoot it - that's just me.
And, there are many here that will accuse me of saying, "This thread is useless without pictures." (To that, I stand guilty as charged!)

Though defensive violence will always be “a sad necessity” in the eyes of men of principle, it would be still more unfortunate if wrongdoers should dominate just men. - St. Augustine