My opinion - the uptick in AI difficulty, with levels, can vary by what type of victory condition you prefer going after.
For science/space, that game became a bit boring for me. Yeah, you realize you are going to get there... that the AI will have bigger lead to start. It's a little more 'tense' at the end of the game... but I still feel like you can rally from pretty far behind some other AI and 'comeback' during the Mars expeditions. I won 4-5 times on rallying from 'well back'... where it felt like I should've lost by the amount I was behind. And after that, it felt kind of like the AI was just waiting for me to win. So I became bored with science.
Domination, IDK - I don't play it, not good at it. But I believe you either need to take closest AI cities hard & fast (pre-walls)... or just get great at unit-comparison and how to identify AI ripe for battle. (Every time I tried, I send 6-7 units and lose half and then the AI has walls and archers up and it feels like a wasted hour where I have nothing but an inadequate army, LOL).
Religion - the AI gets their religion fast and pushes out missionaries pretty soon after getting it. If you can get a religion and your missionaries as 3rd or 4th religion - you can often try to get to a neighbor AI (who is behind in getting religion) and then just pop two missionaries to convert the city right after forming. I've only ever been FIRST on Deity to get religion with Russia & their lavras. Every other Civ, I'm 2nd-5th... and even sometimes - just to get a religion, I have to go absolutely dedicated on settler/two-holy-sites/shrine maybe capital... and then chop out Holy Prayers - which sucks, but often all Religions are gone by turn 55/60, depending on who is out there with you. (I always pray for original-Kongo nearby & friendly!... and I always curse when I think I've got the 5th/5 religions tied-up only to find out that Arabia has that one buttoned up: Lots of swearing). Religion (like science) got a bit boring for me after a few Deity wins, so I don't do that one any more.
Diplo - meh. All the same. The councils still come up turn 100 (std speed) and then every 40-50 turns. I'm actually a bit curious if there is somebody that plays the game that LOVES Diplomatic victory. For me it was a "I did it" once... and then I was just uninterested to ever try it again. I don't feel like there's any challenge in going for a Diplo victory against the AI. Maybe Firaxis programmed something in how they vote (smarter at higher levels?)... IDK.
Culture. Culture though... ooof. Big difference with level.
That challenge is why Culture victory condition is all I play/go for. It varies greatly by the AI, their land, where they are, how their culture/tourist numbers are moving - all game. You have to track this all-game-long. It's like a 1v7 chess game (if 8 member map). So... now... it's all I go for. And it is VERY different on increasing levels. It was actually a shock for me bc a lot of the way I played lower levels... didn't work well at top level (Deity/8). First of all, if you like building early wonders - you are in for some pain. AI jumps all over early wonders VERY quickly. VERY. Pyramids, Oracle, Etemenanki... if they have a spot for them, they start - and you are fugged. Not getting them. Great Library, Machu Picchu - forget it. (Maus & Kilwa are still very reasonable to get, and very key). Pyramids is gone turn 30-40, if any AI has flat desert in their opening 3 cities. Etemenanki is gone if any have a flood tile, turns 25-40. Oracle, gone turn 45-55 if they have a hills tile. I've seen some YouTubers "run" a fast culture victory where they are getting these wonders post turn60... nope - that's a game where you got lucky or cheesed the AIs or something... bc those aren't typically there after the marks I posted. You could throw all your production and some early chops at those - and then suffer in long-runs from clearing those tiles. A few Civs, with holy pantheons for quick work ethic (or Russia's Lavra, or Babylons 3-hills-mines then IZ game) can generate production fast enough to get one or two of the Ancient era - wonders. Often, it's not worth it to 'go for them'... those wonders either 'fall thru the cracks to you'... and you take them later - or you probably doom your chance at a snowball by investing so much early prod in trying to get ONE. (Every 1/50 games I get Pyramids on Deity simply bc no other AI was near desert, lucky-lucky). But it's tough. I had to re-work the entire way I was playing at lower levels. It still pains me to not get Oracle, but I'm finding I have to do it in 50%-75% of my games these days. Personally - I don't play just to 'win' culture any more - I set my own bar of 200 turns, and I try to do it by then. It's created a whole new fun way to play through various leaders - to win FAST. (I've knocked out 5-6 leaders so far, and it's really helping me work on my overall fine-tuning to know that every turn counts. And this self-challenge has really extended the lifespan of the game's enjoyment - for me.)
Anyways...
I've found - that understanding somebody's preferred victory condition is important... bc those that play science/domination - the way they may have played on Immortal/Emperor still translates relatively well to Deity.
But some of the early game stuff that may work for Culture on Immortal/Emperor... won't work on Deity.
So if you are a CULTURE-person... this is my heads-up that if you plan on stepping up to Deity... you may (or may not) be developing some bad habits on lower levels (that several YouTubers may show as 'this is fine' method of play).
Keep us posted - I'm always interested on learning from threads on this site.
What IS your preferred victory condition planetfall???