How are/would newly discovered Suttas (and Sutras) be dealt with? How are/would newly discovered Suttas (and Sutras) be dealt with, specifically be they of content contradicting -- or even just differing slightly from -- previous material and/or for totally new, original material discovered?
Can example(s) be given on how whatever is done, or not done, happens --  especially any instances kept from the public.
The Pali Sutta Pitaka has multiple editions including the Sri Lankan (PTS), Thai and Burmese (Sixth Council) editions.
Here, I list links to footnotes by the translator (Ven. Thanissaro) commenting on the differences between the three editions for various suttas - SN 42.10, Ud 5.9, Ud 8.6, Ud 3.2, Ud 2.7, Ud 4.8, Ud 1.5, Ud 8.7, Ud 6.10. These footnotes will give you some concrete examples.
The Pali Sutta Pitaka corresponds also to Sanskrit Agamas and the Chinese version of Sanskrit Agamas. There are also the alternative version of the Pali suttas in Sanskrit called sutras.
You can find a very good example in this answer comparing the Pali sutta SN 12.67 with the Sanskrit sutra SF 155 and Chinese Agama SA 288. There's also a scholarly commentary in that answer by Ven. Dr. Analayo.
On this university profile page for Ven. Dr. Analayo, you can find links to more of his scholarly writings, which should give you more examples.
I don't think any such differences are kept hidden from the public. In Buddhism, differences in phrasing is not important, as long as the meaning is unchanged, as evidenced by the following quote from MN 103.

‘The venerable ones agree about the meaning but differ about the
phrasing. The venerable ones should know that it is for this reason
that there is agreement about the meaning but difference about the
phrasing. But the phrasing is a mere trifle. Let the venerable ones
not fall into a dispute over a mere trifle.’