Can I use the same Venu 3 wih two separate Garmin Connect accounts on two separate smartphones?

3721582 said:

Can I use the same Venu 3 on two separate smartphones with two separate Garmin Connect accounts?

No you cannot. Respectively, you can, but it will not work properly. You can use the same watch on two different phones with the same account (which should not be a problem in your situation), though. Preferably, enable the Bluetooth on one of them at a time, to avoid conflicts. 

As for the 2FA - if you enable it, it will apply to both instances.

"Respectively, you can, but it will not work properly"

What would be the problem?

They would never run at the same time.

I can't exactly say why they wouldn't want it to be the same account. I heard a story of military staff compromising a military base by using some runner's tracking app, maybe because of something similar.

Don't know it using two separate accounts would help to avoid that in the first place, but if they are OK with that...

3721582 said:

What would be the problem?

If you use two different accounts, you will never now which data lands in which account. Use just a single account instead!

You could also use just Garmin Connect Web (not the app) on the work phone. Although you cannot sync with it, you can read all the data on it that you synced with your private phone.

3721582 said:

military staff compromising a military base by using some runner's tracking app

That was as a result of runners on the military base using Strava, thereby compromising security with their running tracks being part of the Strava Global Heatmap. 

Aggregated Data Usage Privacy Controls – Strava Support

Hmm... no way to control that?

What if I unpair the watch from the one phone before I pair it with the other one?

You can, but in that case none of the accounts will have your complete metrics. You will have a part of the daily HR, steps, Calories, Intensity Minutes, etc in one account, and another part in the other one. Not sure what it would be good for,  but if it is what you want, then go ahead.

So basically all the metrics while at work would only be in that account and all the metrics while not at work will be in the "private" account?

Could I then enable 2FA for the one account and leave it disabled for the other one?

3721582 said:

So basically all the metrics while at work would only be in that account and all the metrics while not at work will be in the "private" account?

Not really. Some metrics like the steps, HR, floors, Intensity Minutes, Calories, sleep, and perhaps a few others are "volatile" - they are deleted from the watch each time you sync the device with Garmin Connect. Others remain on the watch either permanently, or are stored in the activity files which remain on the watch even after syncing (unless you delete them manually). That data would propagate to both accounts.

3721582 said:

Could I then enable 2FA for the one account and leave it disabled for the other one?

Yes, you can set up 2FA individually on each of them. However, having two accounts will still not prevent Garmin Connect or Strava from disclosing your location if you share some activities, or if you enable the Popularity Routing feature in either of the accounts (as noted by seilogramp), so even with 2FA, it would remain a security concern.