It took a bit to figure out, but I enjoyed it once I knew what I was doing. My first playthrough I only managed to win one fight, after losing twice, and then lost again. The next playthrough I did a burn build and was able to win without losing any fights. I liked the flavor text, though there were a number of typos/misspellings.
On the topic of restarting, I was not able to play again after winning or losing, unless I refreshed the page. It did let me click to start, but things were broken in the game. My first time restarting I got to the first shop, but it was empty. Using reroll still left it empty. When clicking to move to the next area, it popped up a warning about having not done everything. After winning I restarted to verify things while writing this and chose the "Relic & Coins" bonus to start, then clicked "Relic", which took me back to the previous screen. It was an infinite loop. Choosing "Coins" worked, and after that I could click "Relic", but the next screen showed an empty area.
I like that you have the tutorial info popping up on the first visit to screens, though there is a lot to take in when first starting out and not all of it makes sense right away. Having the button to be able to pop them back up as needed is nice. Still, even with all the help, I was a bit confused and thinking I must be missing something when the first area did not have a fight. It might help to add a note that the areas alternate between combat and non-combat, with the first one being a non-combat area.
When buying from a shop that has a full inventory, if you leave and come back, it fills in the spots where you bought things. I don't recall seeing anything mentioning that. I also did not see anything that looked like a scroll button, if there is meant to be more you can access in those cases.
When getting to the first fight I had missed the button to start combat for a bit. It would be nice if it had a gentle pulsing effect, or you had the help popups when you get to it, to draw the eye, and perhaps give a bit more info on the combat and the combat specific buttons.
The first time I chose to get a relic I already had, I thought nothing happened. I had not acknowledged the colored borders on them (or the cards) at that point, and mousing over the text said the same thing as before, including the same amounts. It would be nice it the text was updated to reflect the relics being upgraded. I later tested by watching a card I knew would be affected by the relic to be sure it changed when chosen, and it did. It was at that point that I also noticed the border change. Relics are often chosen during the level up, and I think the semi-transparent overlay covers up the flashing effect that happens when it is upgraded. I'd either do something to make the effect rise above the panel, or make the effect last until after the covering was gone and the player would be more likely to see it. The text updating would be the most important as the effect won't matter as much if the player can mouse over to confirm the changes from their choice.
On leveling up, I noticed that parts of the UI looked to get too tall for the viewport resolution. The top and bottom parts of the UI shifted away so they were slightly off screen. This was not a big deal since everything you needed for the level up was accessible, and it all shifted back as that popup closed. After reaching level 9, the level up screen showed progressing from 9 to 10, but after it closed I still saw the level as 10, and each level up after that was the same. I still got level up bonuses, so it wasn't a big deal.
At various points I also had the hover effects not working. Sometimes I had to click in the nearby bit of background and then mouse over again, or just move the mouse around a bit and then back again.
I'm not really a fan of the transition effect with the black coming in part way, then rebounding a bit before continuing. It's not a major thing, but as a personal preference, it was something that I just did not like each time it came up. It wasn't so often that it is a big deal, but since your question was a focus on UI/UX, I figured I'd mention it.
Overall, well done.