Tracing memory usage with &cache_blocks=0&keep_show_loading=1 I see:

block: main_staff_checklist (7 MB used, now at 22,872,864)
block: menu (34 MB used, now at 60,744,016)

The issue is prompted by this in the test code:
// We need to be compatible with low memory limits
if (memory_get_usage() < 30/*a little give*/ * 1024 * 1024) { // If not already in a high-memory (raised-memory) test set
@ini_set('memory_limit', '32M');
set_value('memory_limit', '32M');
}

Which is cleaned up at the end of the test code:
delete_value('memory_limit');

But if it crashes part way, the lowered setting is left there.

I want us to pass all automated and testing in a 32MB memory limit still, so I will see if I can optimise this.

I've optimised the blocks down successfully...

main_staff_checklist: 4MB
menu: 18MB