Page 2 of《泰国的西南官话》by 肖自辉 has this little little insert, which is quite nice:
- Malaysia speaks: Hokkien, Teochew, Cantonese and Hakka.
- Singapore speaks: Hokkien, Hakka, Cantonese, Teochew and Hainanese
- Indonesia speaks: Hokkien, Hakka, Cantonese and Teochew.
- Brunei speaks: Amoy and Hakka.
- Philippines speaks: Hokkien and Cantonese.
- Vietnam speaks: Cantonese, Teochew, Hakka, Southwestern Mandarin, Hokkien and Hainanese.
- Laos speaks: Teochew and Southwestern Mandarin.
- Cambodia speaks: Teochew.
- Thailand speaks: Teochew, Hakka, Cantonese and Southwestern Mandarin.
- Myanmar speaks: Southwestern Mandarin, Hokkien, Cantonese and Hakka.
It's not that surprising to see Cantonese and Min, along with its other branches, getting big representation. Southwestern Mandarin on the other hand is a bit of a shock.
The effect of Chinese characters on Japan and Korea
this is the effect of Chinese literary language on the Korean and Japanese languages, while the question talks about actual Chinese languages spoken in SEA - which, apart from Vietnam, have little effect on the literary languages of SEA, and remain primarily Indic-influenced to this day. There's two different concepts going on here.