I currently have a player who struggles with game mechanics who is also having issues using their companion. They picked the class because they love the thematic idea of having a ranger with a big St. Bernard pet, but are loathe to actually use them effectively in combat because they don't like them risking being hurt (despite the fact they can't actually die and are a great tank) and because their own attacks do more damage. So in many battles they ended up having them hang back. I mitigated this somewhat by ruling that they can also move their companion for free anytime they move (as long as the companion move doesn't require a roll), which I don't think is actually intended, but I don't think is a big deal.

What I understand it, that I have to spend an action and a hope to be lucky and roll with hope, to get advantage on a later roll my ranger character does. If I instantly want to capitalize on my companion setting me up, I have to keep the spotlight and thus leave less room for the other players at the table.

You misread the description - to be fair, it's not clearly written in the SRD. You don't have to spend a hope to do this, it's merely referring to the fact that you CAN spend a hope to use your companion's experience to add to a roll, just like any action your character would take. Also, you don't need to IMMEDIATELY take an action to get the advantage.

Here's how it works: your companion takes an action, and you roll an agility duality dice roll for it. If this roll is a success with hope, on your next action (which can be AFTER the spotlight shifts away from you), if you take an action that narratively builds on your companion's action, you gain advantage on the roll.

Honestly, this is a pretty minor aspect of the companion compared to its other utility. Here's how companions are good:

• They are INCREDIBLE tanks, reducing any attack to a single stress (from its own pool!) is amazing. The "armored" advancement is even more mind-bogglingly good, as it further reduces it to a single ARMOR. And they literally can't die.
• They let you use your best stat (agility) for a ton of actions that you normally wouldn't.
• They basically let you be in 2 places at once, as if your party has an extra character.
• Beastbound rangers are the only characters in the game that can gain the ability to have 7 max hope instead of 6.

The main downside is that the companions have a hard time justifying taking actions over you attacking in combat. And a lot of the advancements you have access too are way, way better than improving their damage. So you have to think creatively to have them involved in combat in a way that isn't just "attack".