The wood replacement siding you need with the double face and the large bull nose is pretty specialized. I doubt you will find any matching at any of the big name builder / Home improvement centers. They may be able to order it for you or you could see if a company like Buffalo Lumber company who shows 3 different sizes of it on line could help you find a source. They have a min order amount of $2500 so that’s kind of out of your range I would think. At least you could print out their two profiles so you know what you are looking for they make a 1x6 and a 1x8 version. Here is a link.
In the past I have went to an area on the house that isn’t noticeable like the back or far side and carefully removed the siding and then used it to make the repairs elsewhere on the house. Then replace that whole area with something that wont break the bank and I could get locally that was close. Maybe a plain taper siding. Sometimes you will find what you need that’s close and you can rip the width to match the revile on the rest of the house even if the form is different.
Yours doesn’t look real bad but looks like it has come un-nailed maybe you just need to clean it up refit it and nail it back up.
Of course there are dozens of methods of doing the repair and mine was heavily weighted to a restoration approach. The town I live in is filled with these circa 1800 homes and the vast majority of the ones that get worked on my own included get covered in fan fold insulation and vinyl siding. In today’s world almost no one wants to maintain a painted wood home. They are beautiful and they will also wear you down with work.
Piecing in straight cut siding with that contoured bull nose stuff is going to look bad even from the road. If it is anything like the ones I have had the bottom 4 feet take a beating along with the south side and of course the end cuts at the corners and around windows and door go first as no one keeps them sealed up.
Chances are there is no insulation in the walls or even sheathing on the outside. That air flow is what kept them going so long. 100 years is a long time though.