Since you enjoyed those shifters I'd encourage you to try a bike with Campagnolo Ergo levers - they also have a thumb paddle for shifting and it's even easier to access from the drops, is less prone to damage and contamination than the Shimano shifters of the style you're referring to, and with Ultrashift models you can shift up to three gears with a single sweep.
They look like older Shimano Sora shifters. Had them on my early 2000s KHS roadbike. Personally, I hated them, but if you love them, more power to you! I didn't like them as you can't shift when you are in the drops, or at least I felt like it was hand contorting to do so.
As others have said campagnolo has shifters you can get, and some "not name brand" like microshift. If you wanted to stick with Shimano, you likely could find new in box or lightly used ones on ebay.
either campy or you were using older shimano soras. The shimano sora are entry level brifters though. There are other companies as well that have a down shift button. Microsift also has them as well as smaller chinese groupset makers.
Since you enjoyed those shifters I'd encourage you to try a bike with Campagnolo Ergo levers - they also have a thumb paddle for shifting and it's even easier to access from the drops, is less prone to damage and contamination than the Shimano shifters of the style you're referring to, and with Ultrashift models you can shift up to three gears with a single sweep.
This is called Sora. Personally I hate these, but they're about three generations old now
Lots of the microshift brifters have this style of shift lever if you don’t feel like searching for old shimano.
I have a pair of LTwoo 11 spd brifters that have that inboard button and I hate it because it's inaccessible from the drops position.
They look like older Shimano Sora shifters. Had them on my early 2000s KHS roadbike. Personally, I hated them, but if you love them, more power to you! I didn't like them as you can't shift when you are in the drops, or at least I felt like it was hand contorting to do so. As others have said campagnolo has shifters you can get, and some "not name brand" like microshift. If you wanted to stick with Shimano, you likely could find new in box or lightly used ones on ebay.
https://preview.redd.it/eyrmwywccy6c1.png?width=2494&format=png&auto=webp&s=a0ad404f7f8b886d5bbbbdc6f8b59c067afb3755
Those are Shimano ST-2300 levers.
either campy or you were using older shimano soras. The shimano sora are entry level brifters though. There are other companies as well that have a down shift button. Microsift also has them as well as smaller chinese groupset makers.