I'm trying to find a short SciFi story
"Metamorphosite" by Eric Frank Russell.
Probably published in the 60s or 70s.
First published in Astounding Science-Fiction, December 1946, which is available at the Internet Archive. Reprinted a number of times over the years; any of these covers look familiar?
Probably < 10 pages.
"Metamorphosite" is a novella, 50–60 pages in length. You described the last part of the story, where the Terrans are brought before the Council of Action.
As best I can remember, the story takes place in a room where a panel of a half-dozen non-human members of the "Galactic Empire" (or some such--probably not quite right)
A majority of the Council is human. (However, I should point out that there are two human species in the story. On the one hand, there are the people of the newly-discovered "backward" planet, who call themselves Terrestrials and their planet Terra; they are Earthmen who have mutated into supermen; our viewpoint character Harold Harold-Myra is one of them. On the other hand, there are normal humans like us who run the Empire, descendents of people who left Earth before the mutation.) Here is a description of the Council:
The Council looked small. Its strength a mere eight, all but two of them human. They sat at a long table, the six humans in the middle, a nonhuman at each end. The thing on the extreme right had a head like a purple globe, smooth, shining, hairless, possessing no features except a pair of retractable eyes. Below was a cloaked shapelessness suggesting no shoulders and no arms. It was as repulsive as the sample on the left was beautiful. The one on the left had a flat, circular, golden face surrounded by golden petals, large and glossy. The head was supported by a short, fibrous green neck from the knot of which depended long, delicate arms terminating in five tentacles. Two black-knobbed stamens jutted from the face, and a wide, mobile mouth was visible beneath them. It was lovely, like a flower.
are about to invite a "backward" planet (Earth) that was recently discovered by the Galactic Empire to join the Empire.
The original intention was to incorporate Terra into the Empire, but at this point in the story the Council is deciding whether to destroy the planet:
"We, of the Imperial Council of Action, have decided that the safety of the Empire demands that we obliterate the planet known to us as KX-724 together with any adjacent planets, satellites or asteroids harboring its dominant life form. We are now met to consider this life form's final plea for preservation, and it is the duty of each of us to listen carefully to what new evidence may be offered, weighing it not with favor or with prejudice, but with justice."
The panel members sit in a row behind an “impermeable,” glass-like barrier.
There is a sort of barrier, but it's not glass-like:
Between this table and the staring captives hung a barrier of wire. Harold, Burt and George could see that it was loaded, and their perceptions examined it gingerly. They diagnosed its purpose simultaneously: it bore an alternating current imposed upon a pulsing potential. Two hundred cycles per second, with a minimum pressure of four thousand volts rising to peak points of seven thousand every tenth cycle.
Hypnocast jammer! reported Burt. He was puzzled. "But that doesn't blank neural sprays. They're different bands. Can you hear what they're thinking?"
"Not a thing," answered Harold. "Neither could I get your thoughts while you were speaking."
"I've lost contact too," put in George. "Something which isn't that screen is droning out a bass beat note that makes a mess of the telepathic band."
Sniffing with distaste, Melor said, "This is where I come in. I know what's the matter. There's a Drane in the room. He's doing it."
There’s a bit of description of several (IIRC) of the panel members and their required ecosystems (e.g., I think one is swimming in a sphere of some liquid; there is a reptile-like being).
That part doesn't match. The aliens in "Metamorphosis" have no obvious life support, and the only reptilian beings present are Melor (nonhuman friend of the Terrestrials) and the Drane:
Mental visualization, Harold realized, had proved correct with regard to shape and appearance but had misled him in the matter of size. He'd taken it for granted that a Drane possessed bulk comparable with his own. But this creature was no larger than his fist. Its very smallness shocked him.
It was lizardlike, but not so completely as first appeared, and now that he could see it closely, its tiny but perfect uniform looked absurd. While they regarded it, the thing sat there and stared at them with eyes like pin points of flaming crimson, and as it stared the strange beat note disappeared, a psychic flood poured through the screen and lapped around their minds.
Two representatives—humans—of the backward planet are admitted to the room.
Not two but three representatives of Terra: Harold, Burt and George.
They then change. The reptilian creature begins to sun itself. For the representatives have metamorphosed into pure energy beings of brilliant, dazzling light.
That's the part of your description that reminded me of "Metamorphosis"; but it's the flower creature, not a reptilian, that basks in the sunlight:
The three Terrestrials made no reply. Their minds were in complete accord and their response was simultaneous.
Dykstra sobbed, "Look! Oh, eternity, look!" then sank to his knees and began to gabble. The purple creature withdrew its eyes right into its head so tht it could not see. Burkinshaw's hand came away from the switch; his glasses fell to the floor and lay there, shattered, unheeded. Roka and Helman and the other humans on the Council covered their faces with their hands which slowly took on a tropical tan.
Only the Floran came upright. It arose to full height, its golden petals completely extended, its greenish arms trembling with ecstasy.
All flowers love the sun.