Ihor> Can you: 1. Load your agenda 2. Start 'cpu+mem profiler 3. Rebuild the agenda 4. Share the
    Ihor> obtained 'cpu _and_ 'mem reports

I found an issue.
--8<---------------cut here---------------start------------->8---
void-function org-looking-at
--8<---------------cut here---------------end--------------->8---

Oops. Fixed.
 
    Ihor> native-comp is improving things proportionally. It should actually have higher impact on
    Ihor> lower-end machine. I recommend native-comp unless you update frequently (and hence need to
    Ihor> re-compile using native-comp often).

On my case. My distro which is archlinux-arm aka alarm for 32bits does
not provide the compiled package libgccjit. So compiling it takes
several hours on this little machine. cross-compiling it takes almost
1h, but preparing the machine for cross-compilation takes time also. So
my conclusion is 'it does not worth the hassle'.

Makes sense. 
If you want to squeeze maximum out of Emacs startup and do not update frequently, you may look into https://archive.casouri.cat/note/2020/painless-transition-to-portable-dumper/index.html

Best,
Ihor