yes, they want to see that insurance validity is in agreement with your intended length of stay. Visa will be checked by immigration upon arrival anyway, like in the old days.
they don't ask which visa. They ask the purpose of travel, you can click "other" or "returning to Thailand" (my case) and length of stay you put 365 days. And I uploaded the insurance certificate (the page with the contract number and coverage amount).
When you arrive at the airport, the immigration will ask you to show your insurance paper. If it's valid only 1 month, they will put an entry stamp of 1 month stay (instead of the re-entry permit validity date) and tell you to clear with your local immigration when you get your insurance extended.