Congrats on the new cards.
The Green should not affect your score, so that one you would use, let the statement print with whatever balance, then pay the statement amount by the due date. I have my PRG charge card on auto pay, so whatever is on the statement, AMEX takes that 17 or 18 days later. Just ensure cash is in your checking and you will have no issues.
Using both cards consistently will build your internal score with AMEX and eventually lead to some CLI.
High Bal Jan 2009 $116k on $146k limits 80% Util.
Oct 2014 $46k on $127k 36% util EQ 722 TU 727 EX 727
April 2018 $18k on $344k 5% util EQ 806 TU 810 EX 812
Jan 2019 $7.6k on $360k EQ 832 TU 839 EX 831
March 2021 $33k on $312k EQ 796 TU 798 EX 801
May 2021 Paid all Installments and Mortgages, one new Mortgage EQ 761 TY 774 EX 777
April 2022 EQ=811 TU=807 EX=805 - TU VS 3.0 765