Lashon Kodesh, literally translated, is "Holy Language". Most translate it as "In Hebrew", but, that's not entirely accurate.
I apologize in advance if this sounds obtuse, but, yes-and-no. One could use those names if they consistently produce an accurate conception in the psyche, while they are articulating them. For example: For me, from my culture, if one is looking for "Michael", that one comes from the Song-Of-The-Sea, Exodus 15. That's where I would go to cultivate an accurate conception. However, that may not work for others because the words of that particular song will produce different ideas and feelings to others who do not come from that background. This is why, in Kabalah, it's taught, always pray in your native language. The magic, for lack of a better word, comes from the heart-and-mind of the one who is speaking. Not from the letters. Not from their syllables.
Does Almighty mean Yahweh or just gonna say "I invoke the authority of the Almighty"
The name "Yahweh" means different things to different people. If one intends to speak "Holy Language" for commanding "angels", there is no room for error. It's very precise. It must be 100% correct. But... that "100% correct version" is going to be different for each and every person in each and every different situation.
Maybe this will help?
When something terrible happens, a car crash, a plane crash, someone is being confronted with the very real possibility of their own demise, many people pray to a higher power. These prayers, in those moments, are pure. 100% true. In each and every way. It's because the individual is in a desperate, fearful state. That particular circumstance automatically produces a prayer which is 100% accurate. That's what one is aspiring to when speaking "Lashon Kodesh". The name used is not important at all in those moments. It's the conception in the mind, it's the feelings in the heart. These are the attributes defining "accuracy" in this context.
while invoking The Almighty's authority.
To begin with, an invocation, is something which is happening internally in the heart-and-mind of the aspirant. If I am invoking the authority of the Almighty ( whomever that Almighty is ), I am feeling the weight of that on my own soul, and I am realizing the implications of all of that power, in my conscious mind. It's terrifying to consider. It's like standing in the face of a tsunami. No wonder, the one who is called "Yahweh" was considered a "Storm God" by many ancient people.
just gonna say "I invoke the authority of the Almighty"
Sadly, no. It's not that easy. One would need to, actually accept "the yoke of heaven" on themself, in their own heart-and-mind.
my relationship with Yahweh is not great
Believe it or not, struggling / striving / "wrestling" with Yahweh, is not necessarily a problem. It can be flipped into an asset.