Will any of these make my rosacea 1 worse?

Hey there!
I also suffered from broken capillaries (Telangiectasia) and rosacea;

From your pictures, it doesn't seem like the rosacea is currently active or flaring- which is a great thing, and probably has to do with the topical antibiotic prescription you're getting. What I do see from the pictures is broken capillaries and hyperpigmentation, most likely from years of unprotected sun exposure.

I would say this about the broken capillaries.. no cream will make them go away. If you wish to clear your face from these, I suggest you consider IPL treatment (*or ND-YAG laser treatment, if you feel fancy..). You could likely clear most of the broken capillaries in 2-3 treatments. One treatment of IPL is 100-200 euros, which IMO is a fairly small price to pay for the huge benefit for the skin. Hyperpigmentation is best treated with Hydroquinone, and from my experience, it can be tolerated well by most rosacea skin types. You will need a prescription for this, but you'll see a dramatic change within 2 months. Since your skin is both sensitive and acne prone, I'll suggest asking your dermatologist for 4% Hydroquinone gel. You'll probably get bonus points for integrating the Azelaic Acid (Ordinary 10% every day could do the trick) into your routine, to further enhance the hyperpigmentation clearance.

If I were you I'd switch the eye cream with Ordinary Caffine+EGCG serum.. since it is a more powerful tool to target undereye issues. IMO, including JUMISO cream and the essence probably don't make your skin any favors. Since your skin seems to be on the oily side, I'd skip morning toner and replace it with a high-quality, multifunctional mattifying sunscreen that would double as a moisturizer. Vichy Capital Soleil can be a great candidate for your since it will leave your skin beautifully mattified, has some actives that help oily blemish-prone skin, and has ferments extracts- which could be specifically beneficial for you (the topical antibiotics you've been subscribed are fairly aversive toward your skin microbiome, and ferments extract might help mitigate this). If you want to add some plumpness and hydration, I'd recommend the good old Vichy mineral 89 serum, since it provides great nourishment of micronutrients for the skin that seems to help rosacea. An alternative to the Vichy serum would be the Ordinary buffet, especially the copper-peptide version- since the formulation suit better oily skin.

I also have mild Type 1 rosacea, which I feel I have gotten under control after trial and error and on a budget!

I would get rid of the glycolic scrub, as it has many irritants for rosacea. The La Roche Posay may be good if you are acne-prone, but salicylic acid irritates rosacea too, so maybe just once per week. Azelaic Acid is a great alternative exfoliant and acne-treatment that can be used daily, as it not only mildly exfoliates but is anti-inflammatory and great for calming rosacea! The Ordinary has one that is not bad, and there are other more expensive or stronger ones. If later down the line when you have gotten your rosacea under control, you feel you need to up your exfoliation game, try a PHA, Mandelic Acid or a Lactic Acid once to three times per week (The Inkey List and The Ordinary have good, clean options).

I would also get rid of your eye cream, as it has fragrance, which can cause puffiness. I just started trying the Klairs Fundamental Eye Awakening Gel, and I like it so far. Also, hyaluronic acid can sometimes be inflammatory to some with rosacea, especially if you live in a drier environment. I avoid it completely (which is a challenge, as it is in almost everything), as I noticed it irritated my skin. So you may try setting aside the Ordinary Peptides for a while as well and see how it affects your skin.

The Pyukang Yul toner is good, but you should top it with a cream at night and a sunscreen in the day. I would try the La Roche Posay Cicaplast Baume B5 and the Beauty of Joseon Rice and Probiotic sunscreen personally, and maybe a high-quality mineral sunscreen for around the eyes, like one from EltaMD for example.

If you're interested in ant-aging, I would slowly introduce a mild, alcohol and fragrance-free retinol (I'm trying out Olay Retinol24, but not sure yet if I can tolerate it) or better yet, get a low-strength retinol prescription from a dermatologist, but again only after you stop having rosacea flares. In general introduce all new products very slowly and patch test first.

Personally, for now I would stick with your prescription, the Pyukang Yul, maybe the Salicylic acid cleanser once per week, slowly add an Azelaic Acid and be faithful to your sunscreen, face wash and moisturizer. Hope this helps and isn't TMI! You can check out my two routines for ideas (though I have drier skin) and also Reddit has a thread on rosacea that I found helpful for ideas!