MTU Explanation with VPNs

I have a question regarding how VPNs work in regards to MTU size and over something like the internet.

If I have my MTU set to 1500 bytes and I send a packet to a VPN device it then encapsulates the packet and it now exceeds 1500 bytes. It then has to transmit this packet to the other end of the VPN tunnel and it now has a non-standard packet size of > 1500 bytes. How can you do this over the public internet without all of the routers between VPN devices supporting jumbo frames?

Would it be smarter to shrink my source side MTU or could that adversely impact applications/operating systems that are expecting a 1500 byte minimum?

Lastly, how come sometimes when packets are too big they’re dropped and sometimes they’re just split up?

Thanks!