The government doesn't issue insurance: private insurance companies do. 100% though, as a matter of law, your insurance isn't void if you don't hold a licence: it might make it voidable however if it was a condition of the policy on application and you gave false information. What would render a policy void is e.g. giving a false name or something pretty serious. You don't understand the terminology. A void policy means that the policy is essentially cancelled. Even if you are correct about the requirement to hold a Thai DL or whatever, that wouldn't void your insurance. It wouldn't even render the policy voidable. It might mean that the insurance company could refuse to pay, but even that would depend on the circumstances. Equally, compulsory insurance is almost always issued for the vehicle, not the person driving the vehicle, which is an incidental fact in the event of an accident, and may or may not determine liability.
Yes, you're correct in that under the Special Tourist Visa, which was introduced last year, it is indeed now possible to stay longer than 90 days. It can hardly, however, be described as a normal tourist visa, as it was specifically introduced to deal with the problems brought on by compulsory 14 days quarantine and the effective inability to require tourists to leave Thailand after 90 days which is usually the case. Nevertheless, the comment about people confusing being here for more than 90 days for residency is correct and based on the usual 90 days period under which normal tourists could remain.
Hire scooters will invariably have 3rd party only insurance which is compulsory, and which is very limited in terms of cover (to other parties). It won't cover damage to the vehicle under any circumstance. Big bikes usually have comprehensive policies (1st class) for obvious reasons