You are asking a number of different questions here, for which I'll try to give answers:
1. Does travel abroad while an EU settlement application is pending invalidate the application?
No, travel abroad does not in itself withdraw, nullify, or or invalidate a EU settlement application. This means that provided that the person has a valid passport, and a non-expired residence card, or family permit, then in principle they can travel abroad and back. However, there are other aspects to take into account before deciding one can travel, which you have also alluded to:
2. Does an application under the Settlement Scheme automatically triggers the issuing of a new EU Settlement Scheme BRC card?
No, this is not always the case:
- If the applicant did not have a valid BRC at the time of application or did not use their BRC to apply via the app, then they will receive a new BRC card
- If the applicant already had a valid BRC at the time of application and they used it to apply via the app, no new BRC will be issued. They are supposed to still use the old BRC card, or proactively apply to convert the old card to a new EU Settlement Scheme card
3. Does the old BRC card gets invalidated after EU Status is granted?
No. As said above, if the old BRC card is still valid (if the expiration date is in the future) then it is good for use until its expiration date, provided this was the card used to apply for EU status via the app.
4. What happens if an applicant had a valid BRC at the time of application to the Settlement Scheme, and used this card to apply via the app, but later on, after being issued the status, the old BRC expires?
If the applicant wants a valid BRC, then the onus is on them to apply for a new BRC proactively. No new BRC will be issued automatically when the old BRC expires. This has to be applied for explicitly. Info here:
https://visas-immigration.service.gov.u ... nt-service
5. What happens if someone travels abroad after being granted status under the EU Settlement Scheme, and they don't have a valid BRC card, family permit, or visa with them? Will the electronic status be enough to be allowed into the UK?
Short answer is No. This is mainly because airlines won't usually be satisfied with the electronic status and will usually ask for physical proof of status in the form of a BRC card or visa (the confirmation email is NOT accepted), even if UK border officials would accept it at the border. This is counter intuitive and confusing, but it's sadly true. This is a very cumbersome situation to find oneself in, and the way out of it is to apply for a Travel Permit abroad, which can take a while.
All visa-required nationals are advised to always travel with a valid, physical BRC card with them, and do not bank only on the electronic status when travelling.
Hope the above answers your question.