Seeking Wired Headphones with Bluetooth Continuity Under PLN 300 - Koss BT539iK Review

Hello
My current headphones have arrived and they are already dead, I am also looking for a worthy successor.
I set up a small budget of up to PLN 300.
I am very tempted by the convenience of wireless headphones, but I would not like to hear frequent noises or crackles, which unfortunately often happens in wireless headphones, especially by radio. I use the headphones almost exclusively on a desktop computer, so tying myself with the cable shouldn't be that bothersome.

And here came the question: Are there any wired headphones on the market that continue working after using the bluetooth?
After searching Google, I didn't find much:

https://www.morele.net/sluchawki-koss-bt539ik-189527-1339355/
I don't know if this is what I mean, they are scarcely described.
In addition to them, I found different configurations of modular headphones, but their prices double my planned budget.

Could someone recommend / find me this kind of headphones?

Alternatively, convince me that bluetooth is beautiful and does not hum, and the cables only interfere with the connector and are a relic of the past.
Or that bluetooth is not worth looking at, and I will hear beautiful sounds only through the cable.
When it comes to microphone issues, it is by no means necessary, but would be a nice addition.

Thank you in advance for your advice.

What do you use these headphones for? These just have the ability to work wireless and wired and are praised in reviews for the quality of sound in both modes. But I'm thinking about your approach - won't it be better to buy 2 pairs of headphones? You write that it will not be a problem sitting at the computer with headphones connected by a cable, but you also expect the headphones to work simultaneously wirelessly and wired. That's my advice - take a look first if your sound source will be able to play sound simultaneously via BT and wired, and then look for headphones that will be able to play sound from two different sources simultaneously.

JBL E50BT have the ability to work wired and wireless. As for the sound quality, I had the opportunity to listen only via Bluetooth and their quality is not impressive.

The headphones are not intended for professional tasks. I thought it was obvious on my budget. I don't see the point in having 2 pairs of headphones. I will buy 2 crap cheap pairs for a budget higher than one universal decent. I don't understand the text at all:

"that's my advice - first check if your sound source will be able to play sound simultaneously via BT and wired, and then look for headphones that will be able to play sound from two different sources simultaneously."

I don't want to play audio from two different sources at once. I just want to have good cable-quality sound without interference sitting at the computer with the option of unplugging the cable and moving away from the computer, e.g. by talking on TS or listening to music with a bit inferior quality.

Added to this is the question of whether I can connect these headphones to a computer via bluetooth?

I just don't know if wireless headphones can be of good quality and if so at what price.

Added after 4 [minutes]:

Headphones JBL E50BT are a bit outside my budget, besides, JBL headphones often pay more for the brand than for the quality.

I will add that your comment on them sounds as if you were advised against them.
So you just advise me against random headphones that are out of my budget anyway?

Ritit wrote:

I don't want to play audio from two different sources at once.

Why not? Yet:

Ritit wrote:

with the option of unplugging the cable and moving away from the computer

You write about two different sources in headphones - BT and cable.

Ritit wrote:

Added to this is the question of whether I can connect these headphones to a computer via bluetooth?

If BT on your computer supports A2DP, then by all means.

I gave up my search. I do not want to bother buying bluetooth modules for the computer and charging the batteries. I chose a little larger wired headphones with good reviews at a much lower price. I chose SUPERLUX HD681B semi-open headphones. I currently have a condenser microphone from this company that is simple but works and expects from the equipment.
Thank you all for the more or less helpful answers. I'm closing the topic.