Most of the time, it doesn't matter which it is. Nor that it's even an isekai in the first place. I think about 70%-80% of isekai stories can be rewritten to be more like DanMachi, which has the exact same feel as most isekais without actually being one. In 90% of where it does matter it's just that the MC knows exactly how to construct modern technology only invented in the last few thousand years, like water pumps, crop rotation, or soap.
And in a lot of cases for this specific variant, there's little difference between an actual possession and a reincarnation with memories of the previous life. Sometimes the character herself doesn't even know which it is. The old memories suddenly appear, and the character doesn't know if she just got placed into a body with access to the body's memories, or just remembered stuff.
That's not true. Regarding whether it matters if it's Isekai, the easy trope to use is the "knowledge cheat" Isekai characters get to make modern inventions that just don't exist usually to make money. That this very chapter makes fun of.
But beyond that it still greatly matters, far more than that easy trope. Isekai'ed characters bring regrets, maturity, skilled knowledge and ideology into their new lives. You don't need Isekai to create a MC with a revolutionary mindset or ideology, but there's always a limit you can't go beyond, especially when recreating entire cultures or lifestyles that have no basis in the existing background. In this very series for example, you'd be hard pressed to explain how the scientific methodology the MC uses to efficiently make use of her skills spontaneously gets pioneered by her without Isekai. The scientific method itself technically is ancient but in it's modern form is based on so many bodies of knowledge and method processes that have been cultivated over the past few centuries, by thousands of scientists and scholars.
Whether the person is reincarnated or possessed/teleported also matters. Reincarnated persons are able to blend into their new society and often want to, for various reasons. They are not tripped up by the common sense of their adopted culture, and usually find acceptance easier.
Inserted characters, whether by way of possession, teleportation or otherwise, often deal with unique problems of not fitting in and being an outsider, and it becomes a major part of their character development.
Isekai stories that ignore all this and just give you stories that can fit regardless of how the MC was brought to the world, or even whether they were transported, are often generic low quality stories.