Those screws don't look like replacements, and the ribbing behind the handle usually indicates newer (post 1960) to me. It does not strike me as a vintage quality plane, I am used to seeing the frog mounting points machined, not coated. (2nd pic, 4x nubs above the screw holes)
The lateral adjuster on older brands had unique shapes
Tee shape, Stanley,
Tight U, Sargent (closest to yours)
Twisted tab, Union
Bent tab, Millers Falls
Better details at
Timetestedtools.net/2016/01/26/quickly-identify-your-hand-plane.
(And thanks for posting this question, I found out one I bought cheap is an Upson Nut)
Seeing as how Sargent didn't use the Phillip screws, has the ribs and u shaped lateral adjuster, is why I suggest newer.
I would not be surprised to see yoursvas a newer Buck Bros.
You might try checking the threaded holes in the sole for metric threads, it modern convenient thread sizes. Similarly for the handles.
Either way, if you can get screws to thread in, seems like any non bedrock type frog should fit, then use any blade etc you like, that part isn't too picky, if it all comes together. Caveat, if those online above are too small, things might get odd
