Yes, LLC = GmbH. No, “Scheinselbständigkeit” is not an issue because you are not even considered self-employed legally if you are the owner of a GmbH. See for instance here:
Freelancer können durch Gründung einer GmbH oder AG ihre Situation dahingehend verbessern, dass die Selbständigkeit nicht gegenüber jedem Auftraggeber belegen müssen. Gründen sie eine Kapitalgesellschaft (AG oder GmbH), gelten sie im Sinne des Sozialversicherungsrechts als Arbeitnehmende/r dieser Gesellschaft. Aufträge werden anschliessend immer zwischen dem Kunden und der Gesellschaft vergeben.
The largest advantage is that you have more freedom. You can decide how much salary to receive, which pension fund plan to use (including pillar 1e), and how much dividends to pay out (which are taxed twice, but with a lower rate when paying them out). Personally, I have a pretty low salary (and invest the difference from my company accounts) with the intention to increase that in a few years to create the possibility for (large) pension fund buy-ins. I can then pay myself dividends (taxed at 50% & 70%) and use parts of it for buy-ins. If I renovate my apartment, I also pay myself dividends to use the large deduction of this year. I also gave some more tips here: Road to FI: Entrepreneur (32, F) - #10 by 0xLambda
But the optimal strategy heavily depends on your life circumstances and your canton. I live in a place where the highest marginal tax rate is “only” ~20%, so my ideal strategy may look quite different to someone in Bern.