In 1957, the United States already used the three-axis Baker-Nunn camera to track the Sputnik satellite. It is the start of what is called now 'space situational awereness' (SSA), the surveillance and monitoring of objects in orbit around the Earth. The large field of view of the camera did not impose great demands on tracking accuracy. Later, more sensitive photoelectric detectors with a very small field of view were introduced. Accurate control of three axes was too difficult. This was solved with a fourth axle.
In the 1970s, the Soviet Union started the OKNO project in Tajikistan, building a number of telescopes on 10 three-axis mounts, also with the aim of monitoring satellites. This was not completed until 1994. It is now in use by the Russian army. The telescopes are in use to find and track satellites and rockets. These mounts are equipped with precise encoders that enable precise control of the axes. You can start your search on the internet for your self with terms like "Optical-electronic complex OKNO Nurek Tajikistan" or "ОЭК ОКНО Нурек Таджикистан".
Tracy Wilson showed his three-axis mount on the cloudynights forum in 2004. His mount was fully motorized, but it missed the great precision in the control to do long integration astrophotography. Steve Joiner wrote a beautifully working simulation program in 2006 to control a mount like Wilson's. The price and availability of accurate encoders and processors apparently hindered the development of an astrophotographic mount.
Mel Bartels has built a three-axis mount intended for manual use with a large Newtonian telescope. It is a Dobsonian-like alt-alt-azimuth platform where both altitude axes are somewhat limited in the angles they can turn. His choice to limit the corner freedom is beneficial for the construction and poses no problem for visual use.
In 2019, Denis Moret described on the French-language forum webastro.net how he built a mount, inspired by Tracy Wilson's concept. This mount apparently also lacks an accurate computer-controlled drive.
The ASKAP satellite dishes - part of the Square Kilometer Array project - are known as three-axis. However, this mount is a classic alt-azimuth mount. Where optical telescopes have a field derotator rotating the camera, here there is an antenna (feedhorn, LNB) in the focus that can rotate +/-180 degrees. This mount therefore has a blind spot in and near the zenith.
For the British Clover project , a mount was proposed for measuring cosmic microwave background (CMB) radiation. The mounting was a true three-axis mount, but certainly not ideal. The telescope and mount could not be intrinsically balanced, therefore much more countermass would be required than the design suggested. This would require bearings and a drive that can move this extra mass neatly. Because the telescope was not placed between but above the elevation axis, it also required a larger building. The orientation of the axes also misses important opportunities. If the telescope should follow a moving object near the zenith, two axes (almost) coincide. Given the limited speeds of motors, this would lead to gimbal lock, in other words a blind spot near the zenith. A solution for some difficulties could be found by a fixed rotation by 90 degrees of the axle between the fork and mounting the telescope in such a way that the optical axle is at 90 degrees from the rotation axle in the current design. This adaptations wold require large counterweights. The project was canceled due to lack of funds.
There are also three-axis motorized Gimbal Mounts offered for camera's, for example by OES . The mount is similar in design as the one of the Clover project, so it can be adapted to a true three-axis telescope mount with many of the beneficial properties, but it will require counterweights.