They just introduced a new interpretation of foreign-sourced income taxation. It would be somewhat surprising if state enterprises accepted foreign credit cards now. You can set up a direct debit from your Thai bank account.
If the German tax rate is higher, it may be likely that you won't need to pay any Thai tax whenever you remit your money. That would make sense. But I think we need to wait for guidelines and clarifications.
If you keep your German dividends in Germany without ever remitting them, no problem. They are not taxable in Thailand. However, from 2024 onwards, your new offshore earnings do not become "savings" anymore, even if you wait to remit.
Dividends (or any other money) from 2023 and before are now your savings that are not assessable income for Thai income tax purposes. From 1.1.2024 onwards, foreign-source dividends you earn while a Thailand tax resident will not become tax-free savings but will be taxed if and when remitted to Thailand.
I believe tax credits will only be available during the year you receive the income, so to be able to deduct German tax you paid in 2024, you might have to remit the money in 2024. But this entire credit system for individuals has not been announced yet.
If you take dividends as a passive owner, you should be able to claim German tax paid as a credit against Thai income tax payable for the amount you remit to Thailand.
If you draw a salary or participate in the management or operations of the German company while staying in Thailand, you need to evaluate whether the company has a permanent establishment in Thailand which would create a tax obligation for your company in Thailand as well.
I uploaded a chanote to the old website, but for the new one it asks for "สำเนาทะเบียนบ้าน ของที่พักอาศัยที่ให้บริการ" which I understand to be tabien baan. I uploaded that (it doesn't even have any name) and was accepted.