will I lose my text messages if I upgrade to a new phone

To additionally help ease her fears, the transfer process actually duplicates (vice moves) the “old” phone data onto the “new” phone.

As long as she selects the option to NOT erase the old phone at the end of the transfer process, her old phone will remain EXACTLY as-is.

Once she’s “happy” with her new phone’s setup - I personally wait about a week - she can then “wipe” her old device as follows:

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

She needn't worry. I get a new iPhone just about every year and every year all my data moves over to the new iPhone. Rudegar provided the perfect link to ensure the seamless transfer of data, including her messages to the new phone.

Since these are important messages, your wife might want to forward the messages to her email for another measure of safekeeping.

On a message which is open, hard press on it. A dialog box will open and tap More..... Now white circles will appear on the left side of each comment in the chat. Tap the circles she wants to save and then tap the forward arrow on bottom right. Now enter the email address you want to forward the message to.

Another simple option is to screenshot the messages, which will save a copy in her Photos.

if one setup the new phone using the own

Use Quick Start to transfer data to a new iPhone or iPad - Apple Support

then all data should transfer