I would describe the language as ingratiatory
To bring (oneself, for example) into the favor or good graces of another, especially by deliberate effort
pleasingly persuasive or intended to persuade
calculated to please or gain favor
This kind of language is not used when the speaker necessarily lacks self-confidence, but rather wants to give the impression ...
I might say "Let's get in touch soon." That is informal and even personal, but it allows for this to be a new friend. I would not use "catch-up" yet, because that implies you are updating previously shared information.
As you have not yet had the initial meeting, to "update" each other is not accurate.
I hope this helps ...