I'm a bit puzzled - I have literally gigabytes of emails downloaded to thunderbird and I don't get any freezes on searching - there's 15 years of emails from my personal domain, plus 2008-2012 of active use and then passive amounts since on gmail, PLUS 3 work domains over several years in that set and I've never had it freeze.
My machine is adequate but not top end (32GbRam, Ryzen 7 3700X, 2Tb NVME/M2 SSD) - it was "good" 4 years ago when I assembled it, it's probably bottom tier by now. Running Arch, but also dual boot Mint - both are fine with it.
Just checked -there's 10.3Gb in the personal domain alone. Have a look at your PC config - unless you have tiny amounts of RAM or are running on a super slow HDD there's something wrong with this picture