In reply to Mark Edwards:
> I like MeMeMe’s solution. But, depending on the diameter of the shaft, maybe a suitable helicoil, epoxy resined into place, would be more exact.
I think if you were going to do that you may as well fill the hole with resin completely, and then when it's gone off drill a new hole.
The nearest thing I can name to what the OP is describing is a 'striking plate' btw, though I know that isn't quite right. Here's an example of a bathroom door privacy bolt supplied with a choice of two such thingamabobs that they just refer to as a 'strike':
https://www.screwfix.com/p/union-chrome-plated-tubular-privacy-bolt-60mm-ca...
Given that it's just a privacy bolt, not a security thing, the hole doesn't really need to fit the bolt neatly to any real depth. It's just there to stop someone opening the door accidentally, not booting it in on purpose.
A rectangular plate with a circular hole would do, no need for the tubular 'insert' bit. The maker of this bolt supplies the thing I'm describing here and calls it a 'flat keeper': https://www.screwfix.com/p/smith-locke-flush-bolt-polished-chrome-150mm/316...
Cutting a rebate to recess a rectangular plate neatly flush with the surface isn't difficult to do with a nice sharp chisel. (All but impossible with a blunt one.)
If the plate is circular it's much more difficult. In a virgin bit of wood you could drill the big shallow rebate to accept the plate first with a flat-blade bit, then drill the hole to accommodate the bolt using the spot where the point of the flat blade bit went as a pilot. With the deeper hole already there probably the only neat way to cut a rebate around it to recess a circular plate into would be using a router and some sort of template clamped in place.