So what is the correct target?
The installed lazarus on your Mac, the one that you have been showing us so far, is x86_64. The FPC compiler it uses is compiled for X86_64.
By 'rebuilding' Lazarus to arch, it has now become an aarch application. Because of how FPCUpDeluxe has things set up the aarch Lazarus will now use the x86_64 compiled FPC command-line compiler and that is exactly the mix that should not happen.
If you think about that for a moment then you hopefully are able to come to the same conclusion as me when trying to figure out what such a mix actually does behind the scenes: making my head hurt

fwiw: the correct target for lazarus of your current setup is x86_64.
The fact that the CPU drop down lists arm and aarch64 as two distinct options doesn't help matter!
That is because strict technically I was wrong naming it arm.
Whenever you see arm the first thought should be 32-bit. Whenever you require 64 bit arm then translate that for yourself to aarch64. The reason to refer to arm was in context to point out that your mac's processor is an arm processor (not a intel/amd/ibm one).
If you, or anyone, could explain to me, in terms no more complex linguistically than "the cat sat on the mat", exactly how I can do this, that would make life a lot easier!
In theory: Just pick what you prefer to use, stick to it and use cross-compiling for all other targets.
The reason I say in theory is because in practice that might be easier said than actually done (cross-target not supported, missing bintools, bugs, etc etc.).
E.g. do note the remarks that Don made about that what he stated that sometimes (cross-)targets are not supported (yet) for certain (host) platforms/architectures. That is either because of Lazarus/FPC itself or due to FPCUpDeluxe not being up to date (at least the version you/we are currently using)
You have at least two targets (windows and linux) running inside a VM based on arm architecture (aarch64 to be correct). Those you can easily test/verify so my initial thought would be to install the aarch64 version of Lazarus with its accompanied (aarch64) FPC command-line compiler (on your mac).
Again in theory (because I lack the hardware in order to test) you should be able to accomplish that by downloading the aarch64 darwin version of FPCUpDeluxe and setup things as you have done before.
If for whatever reason you need/want to cross-compile to windows x86_64 or any other target then you can add the corresponding cross compiler as you have done before (FPCUpDeluxe -> cross tab).
And you can do something similar for x86_64, if you so wish to do so by using the x86_64 darwin version of FPCUpDeluxe and in case wanting to create a setup for both architectures at the same time you can opt for that as well but keep those two installations completely separated form each other. That means that whenever you f.e. want to add another component to Lazarus' toolbar that you would have to do so twice (one for each architecture). In case wanting to add a new cross-compiler for another target and you wish to use that target for both compiler you would have to install that cross-compiler twice. That also mean you have to be very careful to configure FPCUpDeluxe to use the correct Lazarus installation path.