I think there are old school staple guns in CA in the area that includes framing tools.
Determine WHICH staples your staple gun of choice uses before you buy anything. Not all staples fit all guns. Likewise, The length of the staple will be determine by the thickness of your wood chair seat and the thickness of your upholstery fabric. In my experience, the corners need longer staples than the center of a side.
I’ve done plenty of reupolstery work using a trusty hand powered T50 staple gun with its 3/8" wide staples. The staples are available in many different lengths and even different materials. For water craft work where there is plenty of water, use a monel staple. It will resist rust vs the standard iron staple. The 3/8" width of the staple is good for fabric since there is plenty of space between the legs, helping to prevent the fabric from pulling through. The staple used with wood work is often much narrower, and is meant to be pushed into the wood such that the head of the staple is below the surface of the material. I would look for a T50 stapler, either manual or electric. Here’s a video for the Stanley TRE550Z https://www.youtube.com/watch?v=dp56J76lxgk, about $30.