Further (to deal with the language as it appears clearly), the word “bring forth” (yatsa) does indeed come as the “response” to God’s command (or deliberation) in v12, providing (according to John Walton) a literary parallel to show the link of Day 3 with Day 6, where yatsa is used in the command/deliberation, and “made” in the fulfilment.
So to summarise the linguistic features of the three passages:
Vv11-12:
Command/deliberation: “Let the land grow green with grass” (or maybe, to show the Heb construction better, “Let the earth grass over with grass”).
Fulfilment: “And the earth brought forth grass.”
V20ff:
Command/deliberation: "Let the waters swarm with swarms… and flyers (uph) fly (oph).
Fulfilment: “And God created…”
V24ff:
Command/deliberation: "Let the earth bring forth living (beings)."
Fulfilment: “And God made…”
V26ff:
Incidentally, note how the words used for man relate to these:
Command/deliberation: "Let us make man…"
Fulfilment: “So God created…”
About that word yatsa, “bring forth”, used only in the fulfilment of v12 and the command of v24, then. Does it imply merely the “fertility” of the earth, as I suggest, or does it contain deep implications about creative secondary causes? Simply check the closest parallels.
Deut 14.22: "all the increase of your seed that the field brings forth year by year"
Ps. 104.14 (the creation psalm): "(Yaheweh) causes the grass to grow for the cattle, and vegetation for the service of man, that he may bring forth (yatsa) food out of the earth (and wine, and oil, and bread)"
Isa 61.11: “For as the earth brings forth (yatsa) the bud, and as the garden causes the things that are sown in it to spring forth, so the Lord will asue righteousness and praise…” (don’t forget here Paul’s metaphor in the NT about God giving the increase of the soil for both sower and reaper).
Clearly your garden brings forth its Dahlias in the same way that the earth brought form living creatures, as far as the Hebrew goes. As in Genesis 1 generally, the sense is phenomenological, not ontological.
Now to include providence in this in the general sense that “God providentially makes the land productive” is clearly implicit, though of secondary import, in all these texts, where God’s sole Creatorhood is assumed. To go beyond that to give an impression that the land was given a kind of “co-creator” role (perhaps determining what forms the various vegation or animals would take) goes far beyond the text, and miles away from Israel’s theology.