The following two (rather official looking) articles from the old 3.5 archives at Wizards.com provide a quite in-depth look at (the rules for) aerial combat. If you haven't checked them yet, they seem to be an excellent starting point:

Rules of the Game: All About Movement (pt.4)

Rules of the Game: All About Movement (pt.5)

Flying creatures can remain aloft unless their rules says otherwise

The 2019 Sage Advice Compendium contains the following paragraph which directly addresses this situation:

Can a flying creature without the hover trait stay in one place while airborne, or does it need to move each round? A flyer that lacks the hover trait can stay aloft without moving each round.

From the Flying Movement section under Movement and Position (PHB, p. 191) we have (emphasis mine):

Flying creatures enjoy many benefits of mobility, but they must also deal with the danger of falling. If a flying creature is knocked prone, has its speed reduced to 0, or is otherwise deprived of the ability to move, the creature falls, unless it has the ability to hover or it is being held aloft by magic, such as by the fly spell.

Possessing the 'hover' ability prevents a creature from falling when knocked prone or deprived of movement, but otherwise has no effect on where the creature may end its turn. By default creatures that possess a fly speed may end their turn in the air. However, doing so without the 'hover' ability exposes them to falling damage should an enemy somehow deprive them of movement.

Some creatures or abilities may limit your flying ability and require you to land at the end of your turn. See Do I have to land at the end of my turn? for evidence that this is not the general case. One example of a feature with this restriction is the level 14 Path of the Totem Warrior (Eagle) feature which says (emphasis mine):

While raging, you have a flying speed equal to your current walking speed. This benefit works only in short bursts; you fall if you end your turn in the air and nothing else is holding you aloft.

If the feature allowing you to fly does not possess text to a similar effect, you can end your turn in the air or remain stationary while aloft. Having the 'hover' ability merely negates the risk of falling.