Is it wise to limit training others while serving notice, especially when the knowledge wasn't gained at current company?

If questioned, is it fair to say: “This knowledge wasn’t something I gained here, and I don’t feel comfortable training others on external knowledge that I brought in”?

The company pays you to use the knowledge that you have learned before joining this company.

Generally, you should train the junior with the knowledge that you learned from outside this company. When the company hires you, they want to you to apply the knowledge you have learned before joining the company to your work and to train other coworkers.

I don't think you can tell your manager that it is unreasonable for you to train this junior with the knowledge that you learned from outside this company.

It would be a very strange argument to say that you don't want to train this junior because the knowledge you learned was from outside this company. In all my jobs, I have never seen any funny or hilarious arguments like that. :-)

my manager is pushing me to train this junior — but strangely, hasn't asked other team members (who are far less busy) to assist with any training at all.

Have you tried to explain to your manager that other coworkers are less busy, and can train this junior while you have a very tight deadline ?

It could be that the manager understands something that you don't know about these coworkers. Perhaps, these coworkers may not have the strong knowledge that you have learned and become an expert from your previous companies. Or, these coworkers may have been currently assigned other critical work that only the manager may be ware of.

I'm currently under very tight deadlines, working on critical submissions that need my full attention.

This seems to be the fundamental root cause here; too much work, not enough time. Get a clear list of priorities from your boss and explain that you don't have time for all of it. Assuming that only you can do the critical submissions, explain that and ask your boss why the others can't do the knowledge transfer, to de-risk delivery.

If he pushes back, well...tough on him. You're leaving, shortly it will all be his problem and none of it will be your problem.

All the stuff about whether knowledge was gained in the company or not, or whatever narrative is created, seems irrelevant.

There is no benefit to you of pushing back during your notice period in order to thwart some narrative or agenda that your soon-to-be-former manager is pushing. You are leaving and the manager is not. If it is useful to the manager that others don't miss you when you're gone, what do you care? You're gone!

If you enjoy training, and want to spend your notice period doing that, then do that, and be proud of the fact that you can give this junior knowledge they would otherwise not have gained, since those who are not leaving don't know it. If you would prefer to be hitting those tight deadlines on the critical submissions, then focus on that. Since you're leaving, there's nothing much anyone can do to direct how you spend your days. You might as well spend them on the things you want to do most.

Yes, you can have a reputation in an industry. But I'm sure you're capable of leaving a positive impression whether it's by finishing all those critical submissions, or doing a great job training the team that will be doing what you used to do. Be cheerful and energetic, and the notice period will be over before you know it.

my manager has asked me to train a junior new joiner (with just 1 year of experience) on certain concepts that are very rarely used in this company.

but strangely, hasn't asked other team members (who are far less busy) to assist with any training at all.

Have you considered perhaps that your other team members aren't familiar with certain concepts that are very rarely used at your current employer? That you are in-fact the expert in those certain concepts... and therefore these other less busy co-workers just don't have the expertise to teach this junior hire these concepts?

I strongly suspect this is the reason that you are being asked to teach a junior colleague these concepts... Food for thought.

I strongly suspect this is more about creating the narrative that I’m easily replaceable than it is about knowledge transfer.

You are working your notice period. This is definitely about getting someone up to the point that they can replace you (it is why companies have notice periods).

Your job description most likely includes "mentoring junior team members". Teaching a junior team member an unfamiliar concept is mentoring them. A good senior team member helps their junior team members better themselves.

I think the bigger problem is:

I'm currently under very tight deadlines, working on critical submissions that need my full attention.

It is always hard to have a team member leave. Especially one with a lot of experience / specialized knowledge. For me it is strange to see someone working thru their notice period be busy "finishing critical tasks"... As that sounds like a good way to have bugs/critical issues found in whatever that person finished. Without having their experience finishing those tasks to fix the issues. But that is just my opinion coming from a company that tends to have retirees/greener passage seekers spend their notice period transferring knowledge/offloading all of their tasks to team members, and than twiddling their thumbs waiting for those people to ask questions on said tasks. You know, the safest way to handle a teammate leaving. (it is really hard to know what you need to know about a technically complicated job.)

I would ask your manager what they want you to prioritize in your last weeks (or however long your notice period is). And do that.

An employer who hires and retains an experienced person is obviously buying a lot of experience not formed in the current employment, and reproduction of knowledge over a period of time in continuous employment is assumed to be part of the duties of the experienced towards the inexperienced.

So the argument that your experienced was derived before the current employment doesn't wash at all as a general principle.

Obviously if the employer (or a particularly bad manager) is "pumping and dumping" you in an exceptionally exploitative and adversarial way (i.e. in a way designed to undermine the employment or salary, or to avoid paying training consultancy rates, rather than a normal transition between generations of staff), then you might refuse to participate, but this should probably be viewed as akin to going on strike - certainly, it risks being perceived that way by the employer.

If you're overloaded with work in a notice period, the usual solution is to force your manager to choose his priorities and abandon the rest of the work agenda.

In a notice period, it is usually most important to finalise outstanding work, than to embark for the first time on training an unusual skill that isn't even used in the outgoing employment.

It might make sense to try and press the point that you're simply too short of time to train, and render moot the question of whether you are willing to or not.