A reasonable assumption is that your colleague will be tackling a similar project in their new role. There might be other motivations, but it is hard to second-guess them.
If you want to solve the mystery, you could always ask directly "Why are you so interested in my project lately?" - you will need to judge whether and how to ask it, I don't suggest being so blunt as my quote unless there is a casual culture where it is easy to ask such direct questions.
Other than that, once you have spent enough time on giving updates through politeness (depending on your patience and workload - e.g. I might draw the line after a first 15 minute chat about the project), then I suggest you pass the problem of second-guessing the motivation and how much effort to put in, up to your manager.
Suggest to your colleague that further reports/documentation on the project beyond the standups is something you would like to do, but that time for that would need to be prioritised by your manager. Make it clear that he should request your time via your line manager. At that point, if your colleague has a legitimate need in your company's view to learn more about your project, then it can be arranged without problems to your workload. If he does not, then the only problem is you may burn a bridge with your ex-colleague (and he might be asking because he intends to offer you a role or work with you in future due to the project - although beware that could also be a problem for both of you).
