Your TikTok algorithm is messing with your head. IME (3x DC) everything you describe is perfectly normal, age appropriate, healthy development for a baby of that age. It's normal for them to look away for example, because their eyesight isn't very good yet. They can generally only really focus on your face when they are about half an arms' length away (in a standard feeding position). Most things outside this distance range (both closer and further away) are basically a blur.
Speak to your health visitor if you are worried about your baby's development. Please consider stepping away from the apps, and increasing time spent interacting with people IRL - which is not intended to be an insult, it's just one of the best counter-actions to this kind of thing. IME when my babies were little I found mum and baby groups to be very helpful - this helps you make more realistic comparisons, as well as being possibly a source of support. I was obsessed with my babies at that age and all I wanted to do was talk about them, so other new mums who also felt this way were brilliant.
Remember, the algorithms on these apps are trained to maximise the time your app spends open on your phone, that's it. The posts which are most likely to make you keep returning to the app and stay on the app for longest are those which your brain is subconsciously marking as very important information. As a new mother, your brain is also extremely focused on the safety and wellbeing of your baby, so anything which suggests there might be something going on there automatically gets weighted as very important. The brain system which does this isn't especially good at weeding out good from bad information (and the app overrides this anyway) it just stores everything as a sort of "just in case" but this is self feeding. The more you consume it, the more your brain thinks it must be important, and the more you watch it the more it will be shown to you. Over time, even the safeguards of the rational part of your brain get overridden because this part is designed to assess a mess of contradictory information by seeing which bits get repeated most consistently, and so you'll start to feel that certain bits of false information are probably true, but this is simply because they have been repeated so often that it's like they're passing the "rational fact checker" check which was never designed to handle the amount of information you see on platforms like TikTok.
The algorithm is targeting all of this and this exact cycle. It's not designed to increase your anxiety as such. It's just that the makers of the apps don't give a shit whether it's increasing your anxiety, as long as it makes you spend longer on your phone, which you will if your brain (subconsciously) feels it might be important for the wellbeing of your child. The makers of the videos, equally, aren't necessarily targeting these kinds of feelings on purpose, but many of them DO know what kinds of content tends to lead to higher views, and many of them target views and don't give a shit whether their content is accurate or not. Some content creators on these apps actually do purposefully create anxiety-provoking misinformation because they are part of a longer pipeline to steer you towards antivax content and sell you a "cure" for autism. One major way they do this is by highlighting imaginary "autism signs" which are actually perfectly normal development, which many many babies will do. You are in the peak of this target group because your baby will likely have recently been vaccinated, and they can hyper-target this now. Some content creators are well meaning people who have been taken in by this themselves. Some are parents of children who are actually autistic or have other developmental issues and they are genuinely trying to be helpful but their content (which might be accurate, or well-meaning but misleading) gets swept up in this storm of the view chasers and the antivax pipeline stuff.
It's really really easy to get sucked into this, and honestly the best things you can do are 1. Get baby seen by a medical professional, 2. Delete the apps ASAP, 3. Increase time spent with people IRL (IME, preferably people with babies of a similar age), but literally any human contact IRL can reduce the effects of this kind of horrible, pervasive, algorithm-driven anxiety cycle. 4. If the worries persist or they are already extreme, then get yourself seen by perinatal mental health.
Your baby sounds gorgeous and healthy. Please don't get trapped in worrying and let it ruin this time which should be such a joy.