In the share menu I have these options.. Note that you may need to scroll to access all of them..
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Copy
CopyTranscript
Duplicate
Favorite
Move to Folder
New Quick Note
Save to Files
Print with HP Smart (you likely won't have this)
Save to Dropbox (you likely won't have this)
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if Save to Files is not listed, underneath all these options there should be a selection for Edit Actions..., if you tap that a menu will open, make sure the switch for Save to Files is on.
If that switch is already on, I'm not sure why you wouldn't have the Save to Files option. You are using the same Apple ID on both I assume? When you set up the new phone, did you restore from the old one?
If you have both phones, compare the configuration between them in Settings > [your name] > iCloud. In particular I think the new phone would need to have the switch turned on at 'Saved to iCloud' > See All > iCloud Drive.
I don't think this iCloud configuration stuff would cause Save to Files not to show up though as you can still Save to Files to the local iPhone storage and access using the Files app without needing to be synced with iCloud.