Will Apple Watch still mostly-function without an iPhone?

That is a good question. I'm sure it will "mostly" function by itself for some length of time, but the issue is for how long. If you want/need a definitive answer, contact Apple Support.

BTW, you should be aware that you will need to unpair the watch from your old iPhone before you can use it with your new iPhone. Here are two ways to unpair your watch if you no longer have the paired iPhone:

• See the 'How to erase your Apple Watch if you don't have your iPhone' section of:

Unpair and erase your Apple Watch - Apple Support

• With a web browser, go to: https://www.iCloud.com and sign in with your Apple ID. Open Find My iPhone and select All Devices (at the top). Then click your Apple Watch, select 'Erase Apple Watch', and select Next until the device is erased. Finally click "X" next to remove your Apple Watch.

In doing so, you will probably lose any data on your watch after you reset your old iPhone since you will no longer be able to backup your watch. (You may be able to recover older data from your iCloud backup when you setup your new iPhone.). See the 'If you're switching to a new device' section in:

Set up your iPhone, iPad, or iPod touch - Apple Support

Also, before you sell your iPhone, you should read this:

What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch - Apple Support

It it's unpaired from the phone then it is just an expensive doorstop.