here’s another sutta that agrees with the AN 3.100 gold smith sutta about first jhana being weak:,
notice after 5 hindrances, there’s satipatthana practice, and then it skips directly to 2nd jhana, which means 1st jhana IS (or at least it can overlap if one has sufficient passadhi-bojjhanga) the satipatthana supressing the 5 hindrances.
MN 125 excerpt, b.bodhi trans.:
“Having thus abandoned these five hindrances, imperfections of the
mind that weaken wisdom, he abides contemplating the body as a body,
ardent, fully aware, and mindful, having put away covetousness and grief
for the world. He abides contemplating feelings as feelings…mind as
mind…mind-objects as mind-objects, ardent, fully aware, and mindful,
having put away covetousness and grief for the world.1176
23.“Just
as, Aggivessana, the elephant tamer plants a large post in the earth
and binds the forest elephant to it by the neck in order to subdue his
forest habits…and to inculcate in him habits congenial to human beings,
so these four foundations of mindfulness are the bindings for the mind
of the noble disciple in order to subdue his habits based on the
household life, to subdue his memories and intentions based on the
household life, to subdue his distress, fatigue, and fever based on the
household life, and in order that he may attain the true way and realise
Nibbāna.
24.“Then
the Tathāgata disciplines him further: ‘Come, bhikkhu, abide
contemplating the body as a body, but do not think thoughts of sensual
desire. Abide contemplating feelings as feelings…mind as
mind…mind-objects as mind-objects, but do not think thoughts of sensual
desire.’1177
25.“With
the stilling of applied and sustained thought, he enters upon and
abides in the second jhāna…the third jhāna…the fourth jhāna.