I take issue with the “stronger” characterization. Maybe I have a vocabulary problem. However…
Your own perception of the physical world is, by necessity, solipsistic. Your own experience of the physical world is in your own mind. Without that perception, you can’t say it exists.
We know that it’s possible to have this experience of perception without the physical world, as long as your mind exists. In other words, this could all just be a simulation being dumped into your mind without the physical world as you “know” it existing. Hence, idealism.
Whether one is stronger (or more true?) than the other really doesn’t affect how you function within reality - you’re constrained by what you perceive as the physical world.
Indeed. Science isn't the study of the universe, it's the study of our experience of the universe.
Physics tends to imagine that a mind is a neutral blank screen that represents reality faithfully and accurately. But that's nonsense. It's a process that imposes certain kinds of perceptions.
The conceptual metaphors we use - position, mass, velocity, time, causality - are products of that process, not fundamental representations.
It's possible other minds have unimaginably different experiences based on unimaginably different metaphors.
Some of those might have potential mappings to our models, others might not.
Your vocabulary is fine. I think that idealism is necessarily weaker than other ways of viewing the world; it has problems that were repeatedly noted throughout the 20th century in major works by Wittgenstein and Heidegger, among others. (In fact, it can quite fairly be said that most of 20th century philosophy is a reaction to the fuzzy, yet superficially persuasive, idealistic tendencies of the 19th. Analytic philosophy is 100% a reaction to this.)
Per the Wittgenstein, you have, e.g., the "private language" problem: https://plato.stanford.edu/entries/private-language/
Per Heidegger, well, the entire notion of "being-in-the-world" is a response to idealism. This is the notion that we first encounter a shared world of use, tasks, and significance (hammering, writing, speaking with others,) not private "ideas." So the world as you experience it isn't constructed within your head alone; the outside is always with you. You're embedded in an objective field -- or, at the limit, a consensus field.
As a general rule, you can't make sense of science and the commons as purely private occurrences. One's theories are often false; one is often genuinely surprised.
Besides, even classical idealists need something "beyond" representation (Kant's thing-in-itself; Schopenhauer's subliminal Will) to make sense of why experience has the structure it does. That is, the idealist view silently re-imports something non-mental to ground the mental.
Of course, we could be Boltzmann brains, dreaming clouds of charged gas in the sky, or we could be controlled by Cartesian Demons... and that is where strong idealism eventually leads... but I think that these views should be disfavored even on empirical grounds, for instance in your continued existence.