It depends on the country. In SEA for example i choose an area where i want to stay, choose a hostel on agoda for the first days, visit the local cafes or coworking spaces and if i like it and want to stay longer i ask people or look around to find an appartment on a monthly rate

As Franz said, really depends on the country and location.
I find it difficult to find appartment in big cities (even in SEA - Bangkok, Singapore, Kuala Lumpur), so i'm mostly using Booking, Airbnb, Agoda. Same in western europe where monthly rental are not really a thing.

But in smaller cities, i just book an hotel for a few days, sometimes just on arrival, and look for accommodation there, by just looking for rental sign, ask locals, or look for a homestay.

If the homestay solution seems the best one, i often check accommodations on agoda and airbnb and then go there to talk with the owners directly.

Also, local facebook groups could help > in Bali for example, it's used a lot

Like you said, "monthly rental are not really a thing". It's hard to find without being there. I usually look on the internet (mostly France for now, I use leboncoin.fr) but it's time consuming. I always need to explain to people why I do (they don't really understand why I'm looking for a month), I need to negociate the price, be sure there is a good internet, etc.

I'm thinking of an Airbnb just for this: rental for nomads with monthly rates (and other things that matters like a good connection). I'd love it for myself at least, but I guess it could probably be useful to other nomads.

i'd love to get an airbnb like this, but i don't see the value for hosts 🤔
An appartment owner will rent long-term for the peace of mind, or short-term with airbnb for more money. If he doesn't have enough time to manage his airbnb on daily basis, he'd hire an agency for that.
and you get more empty days between guest with a monthly rental, airbnb allow to get a good booking rate.
I can't see a way were this is beneficial for host. Maybe people renting their home only for summer holiday and struggling to find guest the rest of year?

Btw, if you have any tips for finding monthly rental on leboncoin, i might be interested 👍

You're right about the hosts, a lot of them are not interested.

But I still find people on LeBonCoin who are. They like to fill their appartment/home and not bother for a month, it's convenient. I might clarify that I find them not in big cities though. That might be the point: hosts in smaller cities are interested. And like you said, there are also people who rent on holidays and not the rest of the year. Plus, it's cheaper since they usually don't have anyone.

For Le Bon Coin I don't know if I have the magic solution but here's how I proceed.

** I look for a region in particular and I filter with:
- "Locations & Gites" category
- "house" keyword in the search field (bc I prefer looking for a house if that's possible)
- price (that's up to you obviously): you only have week prices unfortunately; so I look above my price cause I negociate a monthly rate after that
- I look for words "wifi" and "internet" in the ad with a good old cmd+f
- See with photos & description if it looks nice and fit my criteria

** Then if like it, I send a message. I have a little "pitch" where I explain what I do (entrepreneur & nomad) very simply (usually I say I have a software company so people understand... People who rent on LBC often are 50-60 and don't really know what are startups and stuff). I ask if they have a good internet connection and insist by saying this is really important to work for me. And I ask for a monthly price.

** Response: first selection is made by people who don't want to rent for a month. Then if they don't offer a monthly rate I don't bother (like some people tell you: week price * 4 > no thanks). When they tell me the price and it's too high I respond something like "Thanks for your response but that's off budget for me". That's when I can have responses by people asking me my budget, and sometimes they adjust their price. If so, sign contract and that's it (then often want paper and check but I propose mail & bank transfer and they usually accept).

What's really missing: A MAP showing all the results > I can't see where the rental is, except by looking one page at a time. Low prices are often in very small cities and I don't want that but I don't have a way to filter (except setting a minimum price but that's not perfect).

As you can see that's time consuming so I'd like to automate this and also curate places that fit that nomad life with monthly rates.

I point out that I've only been doing this for 4-5 months. I always found something good and affordable for now. But I know that might not work this summer. I also plan to keep people's house who leave on vacation and don't want to leave it empty, that's free :)