Is it okay for a potential post doc to send an email to professor on the weekend?
Email is a form of asynchronous communication: it doesn't matter when mail is sent, it can be read whenever pleases the recipient.
High-ranking professionals should not sacrifice their operational efficiency to avoid the possibility of lower-ranking professionals feeling stressed, overwhelmed, etc. by out-of-hours emails. High-ranking professionals should make lower-ranking professionals aware of work-life balance. Managers and subordinates should discuss expectations.
Technology can help. Email should never raise notifications. (They're too numerous and interfere with flows.) Messaging apps can be segregated: Some for work, others for home. (Signal at work, WhatsApp at home, for instance.) Work apps should only raise notifications during set hours.
Only individuals can establish their own, "best" work-life balance.
When you are emailing someone with more authority than yourself (as is the case here), I don't see any problem with doing it outside business hours, provided that you don't ask for an urgent reply and don't blame them for not replying during that time. Of course, sending these emails might communicate some side information about yourself (e.g., that you work during week-ends), but this could be interpreted either way ("passionate about your work" vs "poor/unconventional organization") so I wouldn't overthink it. But don't worry about the effect on the recipient -- if they can't answer during the week-end or don't want to be bombarded with emails at that time, they won't have trouble disconnecting.
By contrast, when you are emailing someone and you are the one who has authority, you should consider the risk that emailing outside business hours could be interpreted as an implicit request to read work email outside of business hours, e.g., "I'm working off-hours so you should do it too". If this is a risk, then it can be a good idea to explicitly say in your email or email signature something like "This message does not require a reply outside of working hours" or otherwise clarifying with your subordinates what your expectations are. But that's clearly not the situation here.
There is an option to "schedule send" an email.
If you are afraid you might forget it or miss some information if you wait till the next weekday, write an email at that moment and "schedule send" at first hours of next weekday.
If you want to add some information, you can also do that before the scheduled time. This helped me a lot.