Japan still has fax machines and 2.5 floppy disks in use with their government and some companies.
So yeah.
Not for nothing but a lot of businesses in the US still use Fax Machines as they are considered more "official" than scanning a document and emailing it. I worked at a law firm for 15+ years and we had to fax pleadings and court documents 99% of the time because they wouldn't accept anything else for remote filing. It wasn't until as recently as 2020 that they finally set up a system for online filing with scanned documents. Old habits die hard and the dinosaurs in some professions cling to outdated tech because they can't be bothered to learn new things and cite "tradition/formality" as their justification.
Either way, it's just a profound lack of creativity and perspective on the part of the author especially when they are supposed to be writing characters that are teenagers.
It's probably more the author giving away their age.
Everytime I see a mangaka not consider phones or video mail as a solution to long distance relationships, it tells me that the author has a few gray hairs IRL.
I don't think Ueno is that old actually (he's listed as 39 on AniList for what it's worth which is not much older than me), it's just more of a case of not really considering modern solutions and instead leaning too hard on tropes like going away for an extended period of time and having someone "wait" for you to return to prove their loyalty or sincerity. As much as literature tries to present novel ideas and concepts a lot of it is woefully derivative and writers frequently take the safer routes which leads to years and years of the same tired plot devices being used over and over again even when it makes no sense.
I mean just as an example, Ueno is also writing Hajimete no Gal where an entire arc was dedicated to ASMR and streaming content. You really think he doesn't know about video calling while simultaneously knowing about streaming let alone ASMR of all things?