As mentioned in the comments, there is a huge range of options depending on what you can afford and consider good.
As you have found, HDMI connections are rare on stereo amplifiers. A surround sound receiver would solve but it seems that it is more than you will need.
Check whether your TV has analogue stereo audio out. This is quite common and it could be connected to almost any stereo amplifier even one from decades ago. The usual type of connector is called RCA and will be two sockets. Most often colour coded red (right) and white (left). Occasionally, red and black. You won't get synchronisation issues with an analogue connection. Here's an example of the cable that you would use.
https://www.amazon.co.uk/TanQY-Gold-Plated-Theater-Consoles-Systems/dp/B0921GMMQ7/ref=mp_s_a_1_1_sspa?c=ts&keywords=RCA+Cables&qid=1679826524&s=home-theater&sr=1-1-spons&ts_id=4085681&sp_csd=d2lkZ2V0TmFtZT1zcF9waG9uZV9zZWFyY2hfYXRm&psc=1
If you can do this then it probably offers the best quality upgrade at a reasonable budget.
Sadly, analogue audio outputs are becoming a bit less common. The Samsung TV in front of me now lacks them. The next thing to look for is an optical audio out (S/PDIF). Converters to connect these to RCA are small, cheap, and easy to find. Here is one:
https://www.amazon.co.uk/DigitalLife-Digital-Analog-Audio-Converter/dp/B0BJT8P2CB/ref=mp_s_a_1_1_sspa?crid=2PMKXVXXIFXHV&keywords=optical+to+rca+converter&qid=1679826771&sprefix=optical+to%2Caps%2C100&sr=8-1-spons&sp_csd=d2lkZ2V0TmFtZT1zcF9waG9uZV9zZWFyY2hfYXRm&psc=1
You will need an optical cable and the RCA cable above. Most of these converters use USB power and might not come with a supply. A spare phone charger should be suitable.
https://www.amazon.co.uk/Optical-WARRKY-Soundbar-Gold-Plated-Compatible/dp/B091GNS8ML/ref=mp_s_a_1_2_sspa?crid=2PMKXVXXIFXHV&keywords=optical+to+rca+converter&qid=1679826910&sprefix=optical+to%2Caps%2C100&sr=8-2-spons&sp_csd=d2lkZ2V0TmFtZT1zcF9waG9uZV9zZWFyY2hfYXRm&psc=1
Now, again, you will be able to use almost any stereo amplifier. You might be concerned about the sound quality of these small cheap converters but they are surprisingly good. If you are discerning enough to be dissatisfied by them then you probably need to spend very serious money.
I am using this system with my bedroom TV. It is connected to an old stereo amplifier and medium quality bookshelf speakers. It is a huge improvement on the TV's speakers at a moderate cost.
In my main listening room, I have an Atmos sound system. Very nice but it cost a lot more.
A bit more
Yet another option is Bluetooth. If your TV can connect to Bluetooth headphones then you could get a Bluetooth to RCA convert e.g.
https://www.amazon.co.uk/s?k=1Mii+B06+Bluetooth+5.0&i=electronics&crid=3D3EMTEI6DCIQ&sprefix=1mii+b06+bluetooth+5.0%2Celectronics%2C94&ref=nb_sb_noss
This is similar to the optical option above. It avoids one wire and might make the physical installation a little easier. However, it will cost a bit more and might be lower quality. Try the ideas in the sequence that I gave them. The first is probably both the cheapest and best (at a budget) and the price goes up and the quality down with the following options.
In all cases, do not expect to be able to control the volume with the TV's controller. None of these budget options will do that. The TV's volume control will do nothing. You will need to use the amplifiers controls.
If your TV has a wired headphone socket then you could try that but I do not recommend it. You would be able to control the volume with the TV's controller but only at the expense of quality.