A word for "mature and stable but neither modern nor outdated"

"established"

Television is an established piece of technology.

I love web browsers because they are well-established

Definition of established

1: accepted and recognized or followed by many people

established rules/customs/traditions

2a: successful for a long period of time and widely known

an established author/artist

an established law firm

… people with Ph.D.s have been credentialed by established experts in their fields — Louis Menand

b: growing or flourishing successfully

an established plant

an established flower garden

https://www.merriam-webster.com/dictionary/established

It's not a single word, but tried and true can be used to describe something that has proven to be reliable or effective in the past. It indicates that whatever you're describing has been around for awhile, and is not terribly modern. Although it may not be the absolute best thing available, it still sees practical use and isn't obsolete.

Timeless.

For example, "A suit and tie is a timeless look."

It is much more common to use "timeless" when discussing styles, like fashion and architecture. It would be less common for technology, but it otherwise captures your meaning quite well.

I think the best option here is established, as answered by chasly, however another option could be accepted:

definition of accept

• consent to receive or undertake (something offered).
• receive as adequate, valid, or suitable.
• regard favourably or with approval; welcome.

for a slightly negative connotation, such as a technology grudgingly accepted for want of an alternative:

• tolerate or submit to (something unpleasant or undesired).