unfortunately the e visa website won't direct you to visa exemption. Lots of information on the Internet is still out of date with the changes that took place in July this year. You didn't need a visa for your travel plans as you and your girlfriend can enter thailand visa exempt
Slovenia has now a 60 day visa exemption which was introduced in July this year. So you are your girlfriend can get the visa exemption as you arrive in thailand.
Suggest you have a look at the hmrc website in the uk. The website will give you information on staying out of the country for 180 days or more. Yes there is an impact on you if you stay out side of the uk it doesn't matter if you work or not. For example you loose the ability to have a uk GP, can loose access to a uk bank account etc. You will become a tax resident of thailand if you stay longer than 180 days within their tax year which is January to January. Uk and thailand have a dual tax treaty which can reduce or mitigate taxes in thailand if you pay tax in the uk. I believe the tax burden is on you not your company if you work remotely I.e. stay in thailand but work for your uk based company online I.e. no work inside thailand.
With a French passport (you and your girlfriend) will get a 60 day visa exemption when you arrive in bangkok. Because you have booked a flight out of thailand within the 60 days to Vietnam then you should have no problems with your airline or in entering thailand. If the airline ask just show them your booking to Vietnam this should satisfy them. If you wish to come back to Thailand after your visit to Vietnam then you will get stamped in again on a visa exemption for 60 days ( your flight from Vietnam may want to see a flight or travel onwards from thailand within the 60 day visa exemption in the same way you have done in entering into thailand the first time
I have used evisa earlier this year and just used the flight numbers of the flights I intended using without purchasing the tickets, I never uploaded any tickets just specified the carrier and the valid flight numbers I only uploaded the first hotel I was planning on using. I would suggest you have done what you think they are asking. My visa was approved 👌
Michael I have typically purchased my flight tickets after gaining the visa. The visa application asks for your flight details which you can get from the flight company, choose the flight you would be looking to use, take a note of the flight number and use that in the application, don't actually purchase until the visa is approved
As a uk passport holder you will get a 60 day visa exempt stamp as you arrive, this can be extended by 30 days at your local immigration for a cost of 1900baht.