I am using Mikrotik access points connected to my RB5009 using the pre-existing wires going through the walls of my house. All the links are established at 1Gbps, except one, between the RB5009 and an hap AC^2 - this particular path only goes up to 100Mbs.
How should I diagnose this and find out more? I am not looking forward to replacing the wire. I could redo the connections on both end of the wire, but I am unsure what is the most effective path forward.

If you use different gear on the same cable, do those negotiate 1Gbps? If they do, it means that all wires are continous. If they don't, then check wire continuity first.
Next thing is to verify proper twisting of all pairs right to last milimetre of cable. Even a few centimetres of untwisted wires before wall outlets or patch pannels can completely destroy cable performance.
Next check proper termination of wires, both ends have to conform to same pin layout (highly recommended are either TIA T568A or T568B).

See what your cable is made of. I had a case of poor quality wiring (CCA) and an outlet that was probably tarnished. After disassembling it, and earning it again, the problem disappeared for a while, but it reappeared. I ended up replacing the cable and socket. I'll just add that it was a distance of about 5 meters.

Rule of thumb for 80% of network problems:

1. If there is a connectivity problem, check cables.
2. If problem still exists, goto 1.

Process of elimination (also suggested by mkx):
move AC2 to a place where you can use another cable for which you know it will support 1Gbps (e.g. swap it with another device advertising 1Gbps, just for testing).
If it does show 1Gbps, there is only 1 factor left.
The original cable.

We have a Mikrotik. The initial cable diagnosis can be done with its cable tester.
Disconnect the other end of the cable from the equipment and test the cable, then repeat on the other side. For a more thorough test, you can make a pair jumper. A piece of cable with a connector or a socket that has each pair shorted.
If the cable is OK, the length of each pair will be approximately the same +/- 2m, and the cable length will be measured the same whether the cable is open or shorted pairs, if there is a problem with the cable/ connectors, the measurements will differ significantly. 100 mbps equipment connected.Disconnected from AC The orange pair is shorted at the far end The link is connected and working

Is this what you mean by a pair jumper?

I just made it and I do not get any result in the cable test section

Some Mikrotik devices do not have a cable tester. Apparently 5009, the pictures show AC2

100Mbps is actually magic number for 2-pair ethernet runs (up to 100Base-TX only pairs 1-2 and 3-6 were used, 1000Base-T requires also pairs 4-5 and 7-8). cat3, if all 4 pairs are wired correctly, can sustain Gbps on short runs (likely possibly with errors in frames which makes switches drop frames), but at least devices can negotiate 1Gbps.

And that's why I was asking my questions in post #2 above (and OP didn't bother to answer to those so I wonder why I'm still bothering with this thread).

Simple process of elimination, my dear Watson

No matter what, there is one final solution ... find someone with professional LAN tester and validate the cable. No amount of spells and incantations will help if the cable is broken.