Although in the past, simple DNS level filtering was common, Telegram's IPs are now blocked at the routing level.
Is Nepal authoritarian? This is a bit complex. If they could or had the ability to enforce all of the laws on the books, then you might be able to argue that.
Nepal is better characterized as loosely anarchic. The country couldn't function if all of the regulations were enforced. What works for them is rampant corruption. This is how things are accomplished. Aside from that, the state institutions are completely inept in almost every way. Even excluding corruption, there isn't enough competence to enforce an authoritarian vision. Nepotism and the other factors you would expect play a role here.
The regulations which are enforced usually relate to opportunities for graft for those tasked with enforcement. Otherwise nobody can be bothered, or they don't want to rock the boat, because the person they'd take action against also has a minister or bureaucrat in their pocket. Easier for them to sit in their gov office, take milk tea, enjoy their benefits and doom scroll the day away.
So while on its face, regulating who can publish a website is an authoritarian affront to free speech norms, it is better understood as a cash grab. Perhaps some high profile journalists might be targeted, that is a recurring issue in Nepal.
Finally, although their Telegram efforts seem to be paying off, this latest effort seems overly ambitious. They have bitten off more than they can chew here. Business is usually conducted with a fair amount of bluster and posturing in Nepal. If tech majors simply ignore it, politicians will lose face. In general, everyone despises them already.
Due to the aforementioned issues, unemployment is a massive factor in Nepal. Money comes into the country from remittance, because doing biz locally is a losing proposition. It is extremely common to see doom scrolling all around Nepal, from the KTM valley to the rural villages. Cutting off YT and FB will create a massive backlash against the universally reviled political classes. It might be hard for outsiders to understand how widely the political class is disliked for their blatant ineptitude and corruption.