Thanks for your patience, I've been seeing if it's possible to trace the maker of your chair, however, to cut a long story short, none of these distinctive barrel back chairs with shaped slats and cabriole legs, has been found with a factory or maker's name, and no records survive as to who made them.
What what we do know is that they date to the first quarter of the 1900s at a time when this barrel form was fashionable and when Arts & Crafts and Mission Oak features were incorporated into the design of factory made chairs such as this one.
Originally, the finish would have been a stained oak or mahogany and looked like this one with a padded and embroidery upholstered seat.
Most of the examples I found in the sales records tended to have structural condition issues, which I notice yours has too (where a steel plate has been added to brace the joint at the top of the back leg) and which seems to be design flaw with these.
As for values, this example, sold at auction for $60 and this example sold for $10 (it was damaged in the same place as yours) so I'm afraid to say the value of yours, without its seat, with a later covering of paint over the original finish, and with the damage to the seat rail is effectively zero, but would certainly make a great foundation for a restoration.
I hope this is not too disappointing and you won't shoot the messenger! But you'd be doubly disappointed if I gave you false hope that it was worth $$$, if and when you came to sell it.
I do hope this helps!
Please let me know if you'd like me to explain or expand on any of the above, I would be glad to.