If a satellite has "escape velocity", it does not complete even one orbit around the bigger body. So, nothing that has made even one complete orbit has escape velocity.
But, that doesn't mean that it cannot get more energy from somewhere and increase its velocity until it does escape. But, last I read, Earth's moon is not projected to ever escape.
Mars having one moon spiraling in and the other spiraling out seems to me to indicate that they are interchanging energy with each other in some fashion. They do have gravitational effects on each other as they have different orbital periods.
Mars does not have the liquid ocean that the Earth has, so it does not have the strong tidal effects that oceans can create on orbiting moons. However, there are still "tides" in the rock of the planets to some degree, so that might have some smaller effect on transferring energy to a moon.
The inner moon orbits faster than Mars rotates, while the outer moon orbits a little slower than Mars rotates, see
https://en.wikipedia.org/wiki/Moons_of_Mars which says:
"The motions of Phobos and Deimos would appear very different from that of Earth's Moon. Speedy Phobos rises in the west, sets in the east, and rises again in just eleven hours, while Deimos, being only just outside
synchronous orbit, rises as expected in the east but very slowly. Despite its 30-hour orbit, it takes 2.7 days to set in the west as it slowly falls behind the rotation of Mars."
and
"Both moons are tidally locked, always presenting the same face towards Mars. Since Phobos orbits Mars faster than the planet itself rotates, tidal forces are slowly but steadily decreasing its orbital radius. At some point in the future, when it falls within the Roche limit, Phobos will be broken up by these tidal forces and either crash into Mars or form a ring.[27][28] Several strings of craters on the Martian surface, inclined further from the equator the older they are, suggest that there may have been other small moons that suffered the fate expected of Phobos, and that the Martian crust as a whole shifted between these events.[29] Deimos, on the other hand, is far enough away that its orbit is being slowly boosted instead,[30] akin to Earth's Moon."
But, it may also be the faster orbiting Phobos that is boosting the slower orbiting Deimos as it repeatedly passes below it. And that may also be slowing Phobos.