There is only theory, the actual science found it doesn't work. There are prostaglandins in semen and prostaglandins are associated with labour starting, but the prostaglandins in semen don't start labour. Some studies show they might even inhibit labour. Bear in mind also, the type of prostaglandin in semen isn't efficient applied to the cervix, theoretically you're better off ingesting it orally. Still won't work but the science is marginally more accurate. See also pineapples. Yes they contain an enzyme which is associated with labour starting but you'd need to eat 8, leaves and core included in one very quick go to ingest enough to replicate nature. You can't do it. It's like poppies can be used to make heroin. So there's theory there but sniffing a poppy won't get you high.
Not sure when the raspberry leaf thing got twisted. It's a uterine tonic meant to make your pushing stage more efficient. In the last few years people have somehow lumped it in with the curry and sex myths and started suggesting it to induce labour. That's not what it's used for.
Of course there's no harm trying anything but I think I'm so opposed to the blithe recommendations because they actually leave women demoralised as they simply don't work. Plus, it's always food you don't want and walking a long way when you're knackered or sex which is agony on your spd. I wish somebody had bandied about cake and tea as the preferred natural induction method.
I also wish we didn't have due dates. 40 weeks isn't a woman's due date. It's slap bang in the middle of the normal 37 to 42 week considered to be full term, with most first babies coming after 40 weeks. They aren't late at all but we do treat women as watched pots. 40 weeks just helps arrange care. Born over the pond in France and you have a 41 week due date. It's somewhat arbitrary.
OP, do whatever makes you happy and comfortable and your baby will come when ready. 37 weeks is early term and while babies born at this gestation have very good outcomes, it's not actually ideal. There is an increased chance of breathing difficulties and lower birth weight which can affect feeding and blood sugar levels. If your baby is happy inside, a few more weeks are nothing but a benefit for them. Good luck!