A word for "mature and stable but neither modern nor outdated"

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).

Enduring

Long-lasting without significant alteration; continuing through time in the same relative state

How about conventional.

Definition from Google:

based on or in accordance with what is generally done or believed.

how about commodity?

in many industries, commodity tech, or commodity processes, are generally considered "industrial strength" and usually lacking "brand new car smell"

Mature is the correct word. When someone says a technology is mature, it in no way means it is outdated or obsolete. Mature only means it is stable and has been well vetted. Obsolescence is an independent matter. For example, jet engines and rockets are a mature technology but no one would say that either are outdated. Obsolescence only happens when a replacement technology comes along and itself approaches maturity.

Robust. " Full of health and strength; vigorous. synonym: healthy." - Wordnik

Legacy - Old, overtaken, but not yet obsolete

2: of, relating to, associated with, or carried over from an earlier time, technology, business, etc.

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

The answer established (by @chasly-supports-monica) seems good to me.

Otherwise, I would also propose tried and true: since it is "tried", it mature and stable, thus probably not modern; and since it is still "true" ("functioning accurately") it is obviously not obsolete.

Tested and proved to be worthy or good. (American Heritage)

Used many times in the past and proven to work well:

A cup of warm milk is my tried-and-true remedy for insomnia. (Cambridge Dictionary)

Those sentences would work:

Television is a tried and true piece of technology.

I love web browsers because they are tried and true tools.

I know a lot of English words. None of them clearly convey all four of the meanings you intend without allowing further unintended meanings.

(We’re still developing vocabulary that includes the assumption that technology has a life cycle. Like the changeover from solids to liquids in language describing the behavior of money, the process will take a while.)

Right now, I’d pick “reliable”. It means we’ve found we can rely on it, which implies that it isn’t new, and that it has worked many times under many circumstances.

Dependable

The dictionary definition for dependable is

Trustworthy and reliable

If something is dependable, you can deduce that not only has it been tested, but that it has also persevered. Therefore, although not necessarily (but presumably) it can be considered "mature", and would definitely be considered "stable".