Ok where is my flameproof suit?
Let's keep it simple and the economics in check ....
Run ANY any ANY decent quality two stroke "low ash" injection oil.
Your wallet will tell you whether you want to run regularly between mineral or synthetic. Pick one or the other based type and stick with it. Do mot mix them. For considerations keep in mind that it is a two stroke and as such the oil is a once through and out the tail pipe path. The more $ you put to the oil the more $ you are just throwing out the back. That doesn't mean used the cheapest. It means be smart, be frugal.
If you or need more then read on.
Try not to get sucked into the TC or TW debate. Here is the run down on current reality. TC is the OLDEST two stroke oil spec. Pretty much all and any oil on the shelf meets TC. They just don't all print it on the jug. TW just means water cooled. It means the oil still flows and performs well at lower temperatures. It DOES NOT MEAN that it will not perform well at higher temps matching and in many cases exceeding the old TC spec.
Realities are that most any if the decent oils you will find on the shelf will meet both TW3 and TC. Only thing to watch for is the "low ash". This is to keep smoke emissions down, reduce plug fouling, and keep rave valves running cleaner. If you do not have rave valves, then you really care even less about ash. Btw ash adds to lubricity
For the record, I run performance power toys and power equipment for 30+years. I know my equipment and do all my own maintenance. I have never had a problem that was oil rooted. I run a decent dino-oil in everything. And whatever labels are on the jug is just what was on at a decent price at the time. BUT ... I never mix different oil brands into the same tank.