A round the world trip for several years or without ending takes a different approach than a shorter trip like a year or something like that.

When we were 26/27 we were able to do a trip of one year (including buying an old Landcruiser and stuff) after my girlfriend finished her study, and I had been working for two years as a software engineer with a normal starting salary. My girlfriend was also working next to hear study saving money, and we had a cheap rental apartment.
Friends who didn't understand how we could pull this off were also saying that we became boring for not going out with them in the weekends (for the period up to the trip). I guess they didn't always get it.

After that, we have been working again like everybody else. Now we are going to do our new trip. Half a year, so manageable in terms of saving.
But we have also come into a position where we can rent out our house with some profit. For the times that we are travelling cheap (only costs being diesel and food) it is already sufficient to keep on travelling.

In the end, this is what you want. A steady income to fulfill your needs (whether at home not working, or travelling)
But when it comes to travelling, it is impossible to determine a generic level of costs. Having long visas or visa-free travelling, travelling slow in areas where food is cheap, fuel is reasonable and you camp everywhere for free, you can keep travelling for ages with little savings.
But yeah, you can also travel in a different style. Much more hotels, visiting national parks (for example in Africa it is expensive), a lot of shipping, or just travelling fast (more fuel and visa cost)

I see people with a huge 4x4 truck with quad and bikes, shipping that huge thing everywhere, visiting several areas twice. Good for them, I think they have an awesome time. But I won't be surprised if that costs like $50k or even 80k per year?
Then you have young people living in a simple van, who barely go out for dinner even though it is cheap. So many different styles of travelling.
Having a pushbike and a tent and a small stove is probably the cheapest way of travelling.