if I get a new phone number will I lose my text messages?

The answer is neither. Your text messages, once received, are associated with your phone. If you sync messages to iCloud or if you back up to iCloud (these are 2 different processes; you can do one or the other) your messages will be restored when you either sync or restore a backup.

If you keep the same phone and switch to a different number by replacing your SIM that doesn’t affect any content on your phone, so you don’t need to restore anything.

If you switch to a different phone with a different number and you transfer content from the old phone to the new phone you won’t lose anything either.

Using the same phone number is more convenient.

You do not need to change your data associated with your Apple ID.

You do not have to tell that you change telephone number to acquaintances, friends, family, etc.

If you are going to switch to a new carrier, ask for number portability (=> use your previous phone number) from your new carrier. 

Your new carrier ensures that your subscription is canceled with your current carrier.

So don't cancel yourself with your current carrier.

This way you will not lose any messages, because they remain linked to your previous phone number.

You will receive a new SIM card from your new carrier, which will fit your new iPhone.

You first have to make an appointment due to the pandemic.

How fast that goes depends on your new carrier.

The above is the method in my country. At that time I had 1 day that I cannot use my phone number.