henrus

Yep travel to Singapore is currently not as easy as it was pre pandemic.

Yes if you want to spend 3 more nights in Singapore you'll have to meet all the Singapore entry requirements again this includes a rapid antigen or PCR test done before boarding the flight to Singapore (note the rapid test can not be done via video supervision and must be done in person by a medical professional/staff there is an exception for some visa holders but not tourists).

Singapore insurance coverage for COVID is only required for the time you physically plan to spend in Singapore. In your situation you will need it for the 1 day you plan to arrive/transit through and then the 4 more days you plan to spend on the way back.

I don't personally recommend any of these insurance providers however the Singapore government lists them as acceptable for meeting the requirements. If you can find one in your home country that meets the criteria of clearly having at least $30,000 COVID medical coverage listed on the certificate of insurance then this is also suitable.
https://www.aig.sg/personal/more-ins...-travel-assist
https://sgtravelinsured.chubbtraveli...g-en/home.html
https://changiassure.changirecommends.com/

It's worth noting that to enter Thailand you will need travel insurance that covers US$20,000 of COVID medical cover whilst in Thailand (this is a condition of the Thailand Pass and will be required for check in at the Jetstar flight counter). I am not sure where you are a resident but here in Australia there are many providers selling covid travel insurance (to Australian residents) and you might be able to find one in your country that covers both Singapore and Thailand for a reasonable price.