Regulations require that if Samui is your first destination in Thailand, your transit flight from Bangkok to Samui must be booked on the same through itinerary as your incoming international flight only on one of the special "Sealed Route" Bangkok Airways flight numbers which are always 4 digits beginning with "51".
The special designated "Sealed Route" flights are only for international arrivals, and are only bookable in conjunction with the international flight. This is to prevent mixing of international passengers (who have not yet had arrival covid tests) with the normal domestic passengers (who do not have such screening requirements) to prevent the risk of spreading Covid from the international travelers to domestic travelers.
The sealed route flights cannot be bought separately and can only be booked by your international airline carrier as part of your incoming single itinerary with your international flight. These special sealed route flights cannot be found for sale on the Bangkok Airways website, since they are not bookable by the public. If your flight number IS for sale on the Bangkok Airways website when you search flights, then it is a normal domestic flight and CANNOT be used for the sealed route. Any similar flight numbers do not count: for example, PG5171 is NOT the same as PG171 which also flies daily.
The 3-island Samui/Phangan/Tao Sandbox requires that the guest book the first night after arrival at a SHA Extra Plus hotel in Samui where they must stay in their room until they get their negative covid test result, before they can continue onward to SHA+ hotels on the other islands.
He said he entered by Test & Go so I assumed he must have had a Thailand Pass. Test & Go launched at the same time as Thailand Pass, on 1 November 2021. It seems he would have had to have a Thailand Pass to enter by Test & Go.
Not being rude, but you really didn't know what a Thailand Pass is? Or you just told them that? It's surprising for any member of any of the Thai visa or travel groups to be unaware of a Thailand Pass as it replaced the COE many months ago as the equivalent requirement document to enter Thailand, and is mentioned in nearly every post in every group for the past few months.
Like I already explained in my comments to someone else in this post, Booking and Agoda are completely different companies that are even headquartered in different parts of the world (Netherlands and Singapore). They are both owned by the same holding company, Booking Holdings. However, each operate independently, and hotels sign separate contracts and offer/manage their listings and promotions separately on the two sites. However, both sites show lower offers, when applicable, from the other site as "partner" listings in order to provide the lowest possible price, in cases where the combination of promotions and coupons offered on one site would result in a lower price than the other. Hotels can also select whether to allow their listing to be shared on partner sites so it doesn't HAVE to appear on the other. The two site's backends are completely different from each other and don't tie together for the hotelier. So it is perfectly plausible to have a problem with one site and not the other. Booking(com) has made a corporate decision NOT to offer Test & Go/Sandbox testing/AQ packages on their site, and to only indicate when hotels are SHA+. However, the rate shown on Booking is only the room rate. So many are booking it and showing up in Thailand with a non-qualified booking that doesn't include the RT-PCR test and SHA+ transfer as required for Bangkok, Samui, and anywhere other than Phuket. Agoda does directly offer AQ packages (and before it Test & Go) so that's why the government is OK with it.
Absolutely, no one is saying they aren't closely connected. But it is inaccurate to say they are the same company. They are separate companies that operate independently and headquartered in complete opposite parts of the world, that happen to be owned by the same holding company. Just like the example I gave in my other post in this thread that no one would say Louis Vuitton and Hennessy (the alcohol company) and Sephora (the beauty/make-up retailer) are the same company even though they are all owned by LVMH.
I already replied why that isn't accurate above. See my comparison above to another well-known holding company which no one would say all those brands are the same company. Here's the wiki on what a holding company means:
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which you can see says it is a company that holds controlling securities in other companies. So it is not accurate to say Agoda, a Singaporean company, is the same company as Booking.com, a Netherlands company. They are under the same corporate group, that's all.
It's more accurate to say they are both under the same parent holding company which also owns Priceline, OpenTable, Kayak, Cheapflights and other websites. But they are run as separate entities with completely different rules and procedures and accounting for each website. It's like saying Louis Vuitton, Hennessy, Bulgari, Christian Dior, Tiffany, Fendi and Sephora are all the same company, just because they are all owned by LVMH. Hoteliers have to sign up separately on Agoda and Booking and have their own accounts for each site to manage their listings, and hotels provide different rates and promotions to each site but have the option to share their listings on both sites which is why sometimes you can place a booking on Agoda and have it send up being served by Booking and vice versa.