In addition to what these articles recommend, you should turn off your device before going through customs. If you decide to power it on or not, that's up to you. However, you should NOT unlock it for the first time.
Your phone (either android or iPhone) forensically has two states - BFU (before first unlock) and AFU (after first unlock). You may not think this is a big difference but it's actually huge. After your device has its first unlock it's much more susceptible to forensic data extraction. The BFU state on several devices is, as far as publicly known, immune to AFU extraction with Cellebrite. Naturally older devices or those that weren't designed with security in mind are susceptible in either state.
Look into GrapheneOS and their user forum if you want to learn more about this as well as what devices have decent protection against forensic data extraction
tl,dr - power off and optionally back on your phone but don't do the first login if you want to deny your device being searched or at least to make it as difficult and as expensive as possible for your data to be extracted forensically.
Source - I'm a cybersecurity professional
OMG I've been waiting for this. The cause will be ...
Obama.
Thanks, Obama!