My favorite modern keyboard is the logitech k780

I'm not entirely clear on the layout you want or the feel or travel distance of the key presses you like, but I am reasonably comfortable that this one checks all your boxes.

https://www.razer.com/gaming-keyboards/razer-ornata-v3-x

EDIT: I would bet dollars to donuts you would love something along these lines if you swapped out the standard keycaps with low profile ones.

https://www.keychron.com/collections/keychron-he-keyboards/products/keychron-k4-he-wireless-magnetic-switch-custom-keyboard

For the key style try looking for "chicklet keys." That's what I've always heard the more laptop-like, flat keys called.

But so many cheap keyboards like what Logitech sells for $10-20 have most everything else you want. Squishy membrane key feel, programmable macro buttons, wired... They're really just not usually lighted and the key roll-over can be quite low.

My favorite keyboard ‘feel’ 100% is an oldschool laptop style keyboard. Like the IBM T60

You may be looking for the IBM SK-8845 Ultranav USB keyboard. They're long-discontinued, but I see several on Ebay.

Razer Blackwidow Stealth w/ rubber o-rings added to the base of each key, which I think is as non-clackety as a mechanical gets.

It isn't. A web search says this uses Cherry MX Brown switches, which are pretty average in terms of noise. Here are some switches more focused on minimizing noise:

• Outemu Boba U4 - a quiet switch with a strong tactile bump (MX Browns have a weak tactile bump)
• Healios v2 - a linear switch (smooth, no bump) designed to be very quiet
• Cherry MX Silent Red - a quiet linear switch you might actually find in a factory keyboard rather than something custom or DIY

At least two of the three use rubber pads inside to minimize noise.

If you actually just want a keyboard for typing words with rather than gaming, stop here.

Keyboards weren't designed with gaming in mind, the layout is terrible, from WASD wasting the ability of your pinky and ring finger to totally wasting your thumb, there's a ton of sideways or angled movement that's just a little awkward. Even 4 directional key movement is such a waste, you dedicate the 4 easiest to use keys, but only use 1-2 at a time, and if you do need 2, it costs an extra finger. If you want a key entry device tailor made for gaming, you need to look at the Azeron Cyborg. Each finger has ergonomic access to 5-6 different keys with only slight movement (you could reasonably press 2 at the same time with 1 finger), while the thumb has access to 3 buttons as well as a hall effect thumbstick (map your WASD to this), all bindable however you'd like, including macros. Angles and distances of the device are also highly adjustable, so it can fit YOUR hand.

This kind of device is, in my opinion, as much an improvement over a keyboard as a mouse is over a thumbstick.

Disclaimer: This is an honest review, other than as a happy customer, I'm unaffiliated with the company. This is not intended to replace a keyboard for typing purposes.

A friend of mine bought a gaming keyboard with magnetic switches (which is a new concept to me). That felt comfortable. I sadly forgot which brand or model it was.

That being said, if you have red or yellow switches, your keyboard should not be clicky. Many mechanical keyboards even have swappable swihches, so in theory you should be able to replace the switches on your keyboard with red ones.

Look at the Periboard-326 wired mini. It's a mesh-chiclet style backlit. I buy 3 of everything usually, backups are always nice, and then years later when you need them, it would be out of stock of course. Anyways, perixx is a German company, and the boards feel great and I use them for gaming no issues.

EDIT: forgot to mention they are priced at $25 or less

From what you want if you dont mind building your own keyboard i would recommend getting a: 60% with hot swappable blank (no switches included) w/rgb backlight, and low profile linear switches.

Tldr. Do some research and have fun building something unique for you.