Nah, that’s not it at all. Looks almost exactly like this Frank Wesson 1870 Large Frame Pocket Rifle Second Type with Stock
Using “pocket rifle” the actual one pops right up.
It’s apparently called the “New Model Pocket and Bicycle Rifle” and was made by J. Stevens Arms and Tool Co.
Ref: https://www.thefirearmblog.com/blog/2022/11/14/rimfire-report-stevens-pocket-rifle/