Both of HP are good, modern look, great display, maybe 13 inch too small ?
Lenovo Yoga also good, but I don’t need touch screen 
Asus Vivobook and ZenBook both are my fav.
14 inch is better to go, especially with 16:10 screen.
I thought also about 15.6 but that can be heavy
The processors are very similar 1.8 -4.3 vs 2.0 -4.5 The 5825U has more L3 cache. Like i say for me i like the vivobook as it is more a typical laptop to me. The zenbook is more an ultrabook with is lighter and thinner and more like an Apple macbook air type. 
I do like 14" laptop over 15.6" myself. The 15.6" have the number keys so it is a bit larger for sure.
I can only say that you are the one going to be using it. Some people are very hard on their stuff and they get broken easily. So how you look after stuff does make a difference as some laptops are very slim and light compared to others.
This one is also nice from Lenovo but is only led screen. IPS panel (Touch Screen)
Edit: Is also heavier weight at over 4lbs.
Is it better to go with AMD Barcelo, Ryzen 7 5825U, 8C/16T
Radeon Vega, 16 GB LPDDR4x-4266 (soldered) or
Intel Alder Lake, Core i7-1260P, 14C/20T
512GB M.2 NVMe PCIe 4.0 Performance SSD, Intel Core i7-1260P 2.1 GHz (18M Cache, do 4.7 GHz, 4P+8E core, 16 GB LPDDR5-5200 (soldered)
Which laptops are these in? They are both very good. I like the Radeon over the Intel Iris graphics. The Intel probably has a small advantage with more cache and higher memory speed. The way the Intel works vs the Ryzen I’d say they are close. Multicore i think Ryzen has the advantage. Either would be a good choice. The only way you could really compare them is side by side with full on tests to really see the difference. It’s not the i9 Intel so i think they are both very close.
Edit: Pci-e 4.0 is faster than Pci-e 3.0 so it also depends what drives are in each.
Edit2: As always in some tests Intel may outperform the Ryzen and on others Ryzen may crush the Intel but some of those tests are beyond the demands a normal user would be doing.
2022 Asus Zenbook 14 UM3402 and 2022 Asus Zenbook 14 UX3402
Vivobook is only with AMD Ryzen™ 7 5800H and HP envy 13 with Ryzen 7 5800U…
Will choose some of them.
Per my research, Zenbook is better, premium model to Vivobook. Rest is the same ,except Vivobook has 2 heat pipes vs 1 on Zenbook. But per reviews, both are really good with cooling.
HP envy is also premium, just 1"smaller
All of them are 16:10 displays OLED, just HP is IPS FHD.
For 300-400 USD more I can buy new Apple Macbook Air Midnight M2/8/256 but I really dont like Mac. I like experiment with Linux, even with Win xD
It seems you leaning towards the Zenbook?
Edit: Check this one out then.
Edit:
Seems good ,but only difference is new CPU and smaller battery, higher price xD
and here mostly available only with : Intel Core i7 12700H
Ya… i here you. Just showing you what’s available here. Certain markets will be limited to models that are different I’m sure.
Yes, my country is very limited with new models. Even if they are available, I think that prices are like 30-40 % higher than in USA, etc
Well i hope you can get the one you decide on and that it turns out to be all that you want it to be.
Do some research on the ASUS. … I have a Zenbook UX461UN that I bought new several years ago … I would love the laptop except that it doesn’t play nice with sleep/hibernate/resume - it never has since it was new. Any time it goes into a sleep state there is no way to wake it other than holding down the power button to force a full shut down, then restarting. I’ve done a fair amount of web searching, tried a lot of different DEs, even tried Windows 10 and Windows 11, it behaves the same no matter what. Some web searching turns up a lot of threads with several folks facing the same problem. It has made me cautious about ASUS laptops and I probably wouldn’t buy another laptop from them. The UX461UN is intel-based, so maybe this is all a non-issue for AMD and related chipset, but you may want to do some web searching to see if there are any sleep/wake issues for the specific model you are looking at.
Thanks about that.
I tried to find some more info about Linux and compatibility with those laptops which I am interested, but for those exact model I didn’t found anything.
Some other models had half working keyboard etc.
Also it depends is it AMD or Intel.
So it is hard to check. I can go with bootable Linux to the store and try but probably they will look at me like an idiot 
Also while my research,I saw that some Intel laptops have issues with Linux and other half are AMD.
So only laptops sold with Linux are problem free, in this case I saw only Acer laptops, which I don’t like 
For me it might be this one maybe?
Edit:
https://psref.lenovo.com/Detail/Yoga/Yoga_Slim_7_Pro_14ACH5?M=82MS00DHUK
or
https://psref.lenovo.com/Detail/Yoga/Yoga_7_14ACN6?M=82N7009MSC
Edit2: My only issue is that it is a touch screen also.
Edit3: It makes it hard for me as i don’t particularly like touch screen.
I like the lenovo laptop except for the touch screen feature.
Yes, yoga slim 7 pro was my fav also, but I found it only as a refurbished with different keyboard than mine lang. So it will be hard for me.
I just found another barebone laptops , here in EU
For example I created this conf and it is almost in my budget, but got 32 GB ram and upgradable to 64 …damn…
https://laptopwithlinux.com/cart-share/ocZI6
Nice …