Stuck on update but says up to date

What iPhone do you have and what version of iOS is it on?

If you have an iPhone 6/6s the max iOS version 12.x, and you won't be able to get your watch to to watchOS 6.x.

See https://support.apple.com/en-us/HT204641.

If your phone is running ios13 then;

This is a known problem ios13 doesn't seem to like watches with watchos5 or below,here is three proven solutions from other forum members.

Quote;

Apple watch 2;

I found a friend, who was on iOS 12 and used his iPhone to pair. Before pairing it asked to upgrade the watch OS (iOS 13 didn't offer this option). After I upgraded the watchos I unpaired the watch from the ios12 phone and then was able to pair it with any iPhone running iOS 13.

Quote;

1st gen apple watch;

pairing was successful on the following device (with associated OS)

to pair via bluetooth I used an iphone 7 with iOS 12, after pairing immediately accepted the watchOS update to version 4.3.2 after everything was successfully equipped with the last update, unpaired the iPhone and the Apple Watch a reset (factory settings) all this took some time but afterwards pairing on an iPhone XR with iOS13 g was a piece of cake.

Quote;

May 9, 2020 4:58 AM in response to Hashimsabbah

Just did this with a series1. I had to pair with the original phone and update the firmware for me to pair correctly. All I did was ask to pair and the update happened on an iPhone 6.

Find a phone with ios12 on it if you can and pair your watch to it,it will ask you to update the watch select yes,after it has updated unpair the watch from the ios12 phone and then pair it with your ios13 phone.

Now you can update to watchos6.

Then I don't have any good ideas for you :-(

You didn't say in your original post (or I missed it) but make sure both the phone and watch are on chargers and charged up over 50%.

Otherwise if you've restarted both I don't have any other ideas.

The Apple Watch Series 0 tops out at watchOS 5 - are you sure don't have a Series 0 instead of Series 1?