Is the oathmagic draining something like the magical potential of practically everyone and concentrating it on the queen and her nobility?
Absolutely everyone who resides within the kingdoms borders and is subject to her laws and under her protection. (something that technically applies to diplomats and weakens visiting mages of other nations)
Peasants usually don't notice the amount of power it's neglible. If you have enough power to cast three spells left per day with some energy left over, and instead you can cast 3 spells per day and be slightly more tired. Practically speaking it barely impacts ordinary people.
Everyone has some magic, everyone gives some. But for most the amount is so miniscule they'd barely notice. Bearing in mind, apart from new conquests, most of the kingdom has grown up not knowing any different.
People with strong natural magic power generally give the same percentage, but because they have more, it's easier to tell the difference.
If you were gonna be a mage, chances are it won't effect you. But law of large numbers, there's enough mages who would just 'barely' scrape by on power requirements, that the oath leaves them just under that threshold. But far more damaging to the mages. You could study from childhood, apprentice under a master for a decade and/or go through expensive schooling, to be a fully trained mage by your mid twenties, knowing all the technical aspects of weaving spells and shaping mana and so on.
Or. You could swear loyalty to the queen, join the royal army or otherwise receive her blessing. And have access to ready made spells which you can cast by instinct. The light magic as bestowed by the oath and the queens blessing is so simple that children can use it, and they do. A completely normal noblechild could wake up today, travel to the queens coronation. Swear her loyalty and receive the queens recognition. And be blasting laser beams from her hand by that afternoon.
It's an extreme example. But you get the gist, if you are born with magical power and want to be a 'mage' you can either study for years and do it the hard way. Or, you can swear the oath and have all the hard parts handled by the ritual. Pretty easy choice.
And even then, plenty of people have magical power, but choose to never seriously develop it, and are quite happy living ordinary lives while the nobility protect them.
And. it concentrates it in the queen. Who then dispenses some of it to her champions. Who, in a bit of a chicken/egg situation. Are normally one flavour of nobility or another.