Looking back to the Spanish flu pandemic and the Smallpox plague, vaccine mandates were used. There are 4 issues that need to be met to justify mandates:
1. Proportionality. Higher levels of risk justify more restrictive limitations on individual freedom, where risk is construed as a combination of risks posed by a disease and the ease of transmission of that disease in relevant local circumstances.
2. Precedent. Precedent set by prior limitations on individual freedom matters: more coercive or restrictive approaches should generally only follow failures of less coercive or restrictive approaches. That is, unless there is an immediate, severe risk, adults should be free to exercise their autonomy to the extent that vaccination rates afford sufficient public protection.
3. Context. Social and cultural context of liberty restrictions must also be considered. In areas where government is unstable or in societies in which trust is fragile, coercive measures could undermine what’s left of a state’s stability or a society’s trust. Liberty restriction and coercion can exacerbate distrust, suggesting the appeal of less restrictive and less coercive education-based approaches. Two drawbacks of education-based approaches, however, are that they might not be trusted by some or might not be sufficiently protective of public safety.
4. Sufficiency of access. Restrictive, coercive legal approaches require sufficient access to the good or service being mandated. That is, it is patently unfair and nonsensical to demand compliance with vaccination policies without making vaccines sufficiently available to those subject to a mandate. This reasoning suggests the importance of the state’s capacity to provide adequate supply for the vaccine for which a mandate creates demand.
https://journalofethics.ama-assn.org/article/when-are-vaccine-mandates-appropriate/2020-01
1) Covid never had that high a level of risk, ESPECIALLY if treated early on.
2) There is no precedent for locking down a nation over a cold virus that the medical community refused to treat until the person was in critical condition.
3) Context. Look at who’s in charge and what they atpre trying to control. Is it the virus? Or the people?
4) The vax is not the only option for treating COVID, nor is it the best one. The government CHOSE to prohibit any other option so as to get their EUA for their ineffective so-called vax.

Given these comparative odds from a peer reviewed paper for the risk of dying from this pathogen, this fails one of the four criteria you listed.
If this had even a 10% mortality rate, there might be justification, never mind a 30% or 40% rate.
But it doesn't. It doesn't not even in the groups most at risk.
If this were something that warranted these unconstitutional measures, an exception could be devised. And mandates wouldn't be required. People would clamor for it, not be forced at the point of a government gun and the loss of their livelihood to submit to it.
People that would support these measures for a pathogen of this lethality, in order to obtain some semblance of perceived safety by forcing these measures on ostensibly free people are not only not conservative, they don't deserve liberty.