I don't mean to be a killjoy but both these quotes are obviously fake for anyone familiar with Plato. (The concept of god was not used like this in Ancient Greece and Socrates didn't talk like that.)
Mistranslated/corrupted:
"No citizen has a right to be an amateur in the matter of physical training…what a disgrace it is for a man to grow old without ever seeing the beauty and strength of which his body is capable."
Closest quote:
"Besides, it is a disgrace to grow old through sheer carelessness before seeing what manner of man you may become by developing your bodily strength and beauty to their highest limit." - Xen. Mem. 3.12
Mistranslated/corrupted:
"In order for man to succeed in life, God provided him with two means, education and physical activity. Not separately, one for the soul and the other for the body, but for the two together. With these two means, man can attain perfection."
Closest quote:
"For these two, then, it seems there are two arts which I would say some god gave to mankind, music and gymnastics for the service of the high-spirited principle and the love of knowledge in them—not for the soul and the body except incidentally, but for the harmonious adjustment of these two principles." - Plat. Rep. 3.411e
Here's one relevant quote from the Memorabilia:
ὁρῶ γὰρ ὥσπερ τὰ τοῦ σώματος ἔργα τοὺς μὴ τὰ σώματα ἀσκοῦντας οὐ δυναμένους ποιεῖν, οὕτω καὶ τὰ τῆς ψυχῆς ἔργα τοὺς μὴ τὴν ψυχὴν ἀσκοῦντας οὐ δυναμένους.
As those who do not train the body cannot perform the functions proper to the body, so those who do not train the soul cannot perform the functions of the soul. (https://en.wikiquote.org/wiki/Memorabilia_(Xenophon))
Socrates was also a foot soldier/war hero who elected to continue to socialize and drink with famous athletes all his life.
Plato’s quote I’m not so sure but there is no shortage of discussion of mind/body, exercise, movement in his works.