First off, I agree that it is hard to hear him (seemingly) push the vax. Why? Because we (rightfully) feel that the truth should be shouted from the rooftops.
So, why does it seem like he is pushing it? To understand the answer, you must remember that we are at war...
Stop and think about what would happen if Trump publicly denounced the vax.
Starting the very next day, the news networks would run nothing but tearjerker stories round the clock about each and every unvaxxed death (real or imagined). They would blame each one on Trump. "Because HE said not to take it, this poor mother of three is DEAD!"
(BTW, the same stories would run even if Trump 'stayed silent'. "Because HE didn't 'do his part', this poor...")
So, to minimize the damage (of this war), Trump prepared the country. For months, he said (to anyone who would listen) that effective treatments existed, the flu was easily survivable, and no one should be coerced into a vax.
How many tens of millions of people learned that the virus was treatable and survivable when Trump 'got sick' in 2020 and recovered just a few days later?
Trump knew this global takeover (attempt) was coming, and he knew that 'resisting the vax' was the key to the whole thing.
He has exposed them by forcing them to accelerate their plan (so that it is easily visible), and has thwarted them by prepping us for resistance (more important than anything). And he is still clearly saying that people should have free choice.
In war, there are sometimes tough choices. Sometimes, there is no 'perfectly safe' choice. Sometimes, you have to save 'as many as you can', so that you don't lose... everyone.
Personally, I'm grateful that we have a leader that is strong enough to make those choices, and smart enough to think ahead and counter a very evil plan.
I completely agree with your third sentence ("With each passing day...")
Which is exactly why it is important not to give the MSM the distraction and change of narrative that they so desperately need.
But we can certainly agree to disagree. I wish you the best.