How much privacy will I lose if I switch to e/OS

Were you using the Google espionage services on GOS? If so, you'd likely gain a little privacy because of µG.

Some devices can lock the bootloader but that's not a generally supported feature on /e/OS.

I recommend sticking to GOS. If you'd like to use something else, I'd recommend DivestOS. CalyxOS, LineageOS, /e/OS and iodéOS are all significant downgrades in usability, privacy and security and therefore not worth using on a Pixel.

it depends.

you'll definitely be loosing security, which can turn into loosing privacy if you get affected by malware.

you'll also be loosing privacy if installing proprietary apps, since GrapheneOS has features like storage scopes and a better permission system that help minimizing privacy issues.

I think that locking your bootloader in a Pixel is possible regardless of the ROM you install.

Anyway, I think that there's no real benefit of installing any other custom ROM in a Pixel other than GrapheneOS. You'll be just loosing out in security and potentially privacy for no real reason.

Not sure if you can relock the bootloader

Their site doesn't include that info

https://doc.e.foundation/devices/panther

/e/ is a "degoogled" experience, but as noted on their site and by others here:

Google Services are replaced by microG and alternative services (see below for more details)

For a regular uninformed user like myself (I just use the stock ROM on my phone because I am stuck with it) I read that as:

We made this experience as frictionless as possible at at a cost.

The friction here would be banking and/or tap-to-pay apps that I think cause some issues for some people (please correct me if I am wrong).

So, you would lose something that is offered by GrapheneOS and gain a different interface and access to apps that have a hard requirement for GSF.

Not much