I mentioned the Berg connector. Here is a glossy description:
https://www.connectortips.com/breakthrough-contact-design-spawned-500m-connector-company/It is made in both a crimpable version for wire to wire or wire to board and a pre-loaded version for board to board. It is very dependable and is the standard for many (most) model servo connectors. There are lots of imitations. Model applications are generally limited to 3 contacts. I routinely use 6-contact wire to wire connectors with Berg contacts.
Digikey carries it, but it seems Mouser has a better stock. Unfortunately, the original Berg company underwent some acquisitions (I would sell out my namesake company for $500 million too). It is currently owned by FCI/Amphenol. Unfortunately as miniaturization keeps getting smaller, the original Berg is too big. Amphenol has connectors with various plays on the name Berg and the datasheets refer to a spring, so I suspect they are similar, but perhaps not identical.
To me, the essential part is the spring contact. Other versions I mentioned also have springiness.
Although it is getting harder to find, if you are interested in 2.54 mm, it is where I would go. For 2 mm, as mentioned, I go to Samtec.