Pins are glued, they won’t just come out. There are tools to remove those pins and you can basically make your own, it’s basically a thin flat piece of metal you shove into each channel to move the retaining tab out of the way temporarily

https://a.aliexpress.com/_mMa3SwF something like this, the ones I have are different, but you can makeshift something in a pinch

But again the adhesive will mean this won’t work unless you cut/remove it. Also are you sure the only thing that’s changed is the connector? The pinout may have changed, the board you’re connecting to may have changed, etc

There are LEDs designed to run off fluorescent ballasts but usually for more standard sizes (like T5). You could search around, no clue what size bulb that is, maybe something exists if you can id the bulb type

Otherwise you could pull the ballast and replace it with a led ballast that runs off 110/220 (whatever your locale uses). These are cheap and easy to wire. Then whatever bulb fits in the space. Just search bulbs before you get a ballast to make sure you get a ballast that outputs the correct voltage

Or just replace the bulb, easiest fix