Vaccination, Ethics and Morals
The monastic rules of the Vinaya has rules pertaining to food, lodging, medicine, conduct etc. There are rules pertaining to medical care. The Buddha ate, slept, wore robes, took medicine when he was ill etc.
The Middle Way of the Buddha avoids both extreme indulgence and extreme asceticism. It includes moderation in food, healthcare and living. To neglect healthcare is to go against the Middle Way of moderation.
From Kucchivikara-vatthu of the Theravada Vinaya, the Buddha taught:

&quot;A sick person endowed with five qualities is hard to tend to: he does
what is not amenable to his cure; he does not know the proper amount
in things amenable to his cure; he does not take his medicine; he does
not tell his symptoms, as they actually are present, to the nurse
desiring his welfare, saying that they are worse when they are worse,
improving when they are improving, or remaining the same when they are
remaining the same; and he is not the type who can endure bodily
feelings that are painful, fierce, sharp, wracking, repellent,
disagreeable, life-threatening. A sick person endowed with these five
qualities is hard to tend to.
&quot;A sick person endowed with five qualities is easy to tend to: he does
what is amenable to his cure; he knows the proper amount in things
amenable to his cure; he takes his medicine; he tells his symptoms, as
they actually are present, to the nurse desiring his welfare, saying
that they are worse when they are worse, improving when they are
improving, or remaining the same when they are remaining the same; and
he is the type who can endure bodily feelings that are painful,
fierce, sharp, wracking, repellent, disagreeable, life-threatening. A
sick person endowed with these five qualities is easy to tend to.

Based on this Vinaya quote, I would say that the Buddha himself would have wanted his followers to practice moderation, and accept the advice of healthcare professionals and the government when dealing with the Covid-19 pandemic.
Of course, they should not accept advice blindly but they should ask questions and clarify their doubts before they accept the advice if they see fit, as taught in the Kalama Sutta (below):

&quot;So, as I said, Kalamas: 'Don't go by reports, by legends, by
traditions, by scripture, by logical conjecture, by inference, by
analogies, by agreement through pondering views, by probability, or by
the thought, &quot;This contemplative is our teacher.&quot; When you know for
yourselves that, &quot;These qualities are unskillful; these qualities are
blameworthy; these qualities are criticized by the wise; these
qualities, when adopted &amp; carried out, lead to harm &amp; to suffering&quot; —
then you should abandon them.' Thus was it said. And in reference to
this was it said.
&quot;Now, Kalamas, don't go by reports, by legends, by traditions, by
scripture, by logical conjecture, by inference, by analogies, by
agreement through pondering views, by probability, or by the thought,
'This contemplative is our teacher.' When you know for yourselves
that, 'These qualities are skillful; these qualities are blameless;
these qualities are praised by the wise; these qualities, when adopted
&amp; carried out, lead to welfare &amp; to happiness' — then you should enter
&amp; remain in them.

Also, spreading misinformation about Covid-19, masks and vaccines is against the fourth precept of not speaking falsehood.
Wearing a surgical mask is more for the wearer to avoid spreading pathogens to others, than for the wearer's own protection from contracting an infectious disease. As such, wearing a mask with the explicit intention of reducing others' suffering, is also an expression of compassion (karuna).
Getting vaccinated with the intention of preventing others, especially the high risk group, from becoming infected, is also an expression of compassion (karuna).
The quote from DN 26 below, also shows that the Buddha did not promote anarchy or civil disobedience. He stated that the wheel-turning monarch should provide just protection and security to his subjects and also care for their welfare.

‘But sire, what are the noble duties of a wheel-turning monarch?’
‘Well then, my dear, relying only on principle—honoring, respecting,
and venerating principle, having principle as your flag, banner, and
authority — provide just protection and security for your court,
troops, aristocrats, vassals, brahmins and householders, people of
town and country, ascetics and brahmins, beasts and birds. Do not let
injustice prevail in the realm. Pay money to the penniless in the
realm.

I would even say that a responsible Buddhist should support his or her government and follow its advice (after clarifying it), if the government is discernibly doing the right thing, and if its advice is in accordance with the five precepts, Right Action, Right Speech and Right Livelihood. For e.g. conscription into military service is against Right Livelihood, and should be declined.