From Tourism Authority of Thailand 

Bangkok, 5 July 2023 – Bangkok has become the first international destination for Malaysia’s newest low-cost airline MYAirline, with the launch of a new daily direct flight from Kuala Lumpur to Suvarnabhumi Airport on 28 June 2023 and a second daily flight to Don Mueang International Airport on 1 July 2023.

From 17 August 2023 a second daily flight will be added to both airports, bringing the total daily flights operated by MYAirline between Kuala Lumpur and Bangkok to four.

The airline, established in January 2021, said it was the first Malaysian carrier to fly to both Bangkok airports, and that it planned to add flights to other destinations in Thailand in the future, such as Phuket, Krabi, and Chiang Mai.

It seems that MYAirline is using both terminals at KUL - i.e. the full service terminal and the low cost terminal, both of which are branded as KUL. It's important to note that it can take up to 30 minutes to get from one to the other, so check on booking which terminal your flight will be using. The half-hourly airport express train from/to the city stops at both terminals. Similarly the regular limousine service from KL Sentral station stops at both.

Surface transport between the two terminals is by bus which departs every 15 minutes. I have no idea what happens if you are entering and departing on international flights using both terminals - e.g. Singapore to KUL using one airline arriving at the full service terminal and KUL to BKK using another airline at the low cost terminal. I assume there has to be a way of transiting without having passports stamped. Best to check.