Paint/plaster texture question
There are a ton of ways to texture wall surfaces (too many to list here), all require some expertise acquired through trial and error and a perfect match is nearly impossible.

Originally, when a craftsman plastered your wall, he likely used a wet float technique that allows the sandy aggregate in the plaster to rise to the surface. That is not a process you can easily duplicate when patching.

Your best bet would be to experiment (on a separate practice surface) with various combinations of soupy plaster or texture paint using thick nap rollers, stippling rollers, stucco floats, etc. Or hire a reputable plasterer or decorator to redo the whole wall when your repairs are complete. Yours is a common problem with no easy solution.