Only a government-accredited agency can evaluate and certify ("approve") to those safety standards, at least in North America.
No self-declaration is permitted there.
It's a long snakey path to follow safety legislation in any country, who is the "authority having jurisdiction", who makes it law that products have approvals. Once I had to convince an asshole CEO that safety approvals were required for some equipment and it was brutal in the USA. Several states
do not have the National Electrical Code in effect so asshole CEO said you can sell anything (electrical) there and no need for engineering to worry
I almost lost my job refusing to sign/stamp that shit.
For multimeters it's certainly OSHA (at work) or corporate policy they have credible safety certifications.
The liability for a product failing a safety claim is what keeps most companies from selling gear with fake approvals. I see a few Japanese companies with no formal safety approvals, only claims to meet x standard.