You can apply starting from October 8. A processing time of 5 working days has been announced for both Hanoi and Saigon. Check their announcement to determine which consulate to indicate when applying, as they have divided responsibilities based on province.
You can apply for the LTR Visa only through the official LTR Visa program website. Once approved, you can schedule an appointment for LTR Visa issuance either at the Royal Thai Embassies or Royal Thai Consulate Generals overseas, or at the One Stop Service for Visa and Work Permit Center in Bangkok.
In your screenshot, it shows an application for an e-visa. However, they will request notification of approval, which can only be received through the LTR program website. In other words, there are two steps: Application Submission (via the LTR Visa site) and Visa Issuance (which can be done via e-visa if available in this country).
Yes, you apply through the BOI online, but you have the option to choose where you receive your visa if approved—either at the OSOS Chamchuri Square in Bangkok or at a consulate or embassy abroad.
You should prove that you fall under the "Workcation" subcategory for digital nomads, remote workers, foreign talents, and freelancers.
What you described is a business, but you can position yourself as engaging in "remote work." This can include self-employment, especially if you emphasize that you sell to clients remotely. If you have a brand, consider submitting any trademarks or related documents.