What data Valoranchi touches
The short version: almost nothing leaves your computer, and the little that does is listed below.
What stays on your computer
Everything the app reads from your account: inventory, skins, store, matches, rank, friends and messages. It is read from the Riot Client you already have open, displayed, and sent nowhere.
Your settings, your saved loadouts and the account switcher's sessions live in the app's data folder, on your disk. The sessions are also encrypted with DPAPI, the same mechanism Windows uses to protect saved browser passwords.
What goes out to the internet
The update check. The app asks whether a newer version exists and downloads it if so. Nothing of yours goes with that request.
A random identifier per Riot account, generated on your PC the first time. It isn't derived from anything about you and can't be reversed into who you are: it exists only so the API knows a request came from a real Valoranchi install rather than from anyone at all.
If Discord activity is on and Discord is running: your Discord user id paired with your Riot account id, so a Discord account can be resolved to the Valorant account playing on it. Your Discord display name goes with it, and the identifier of your avatar, which is what points a browser at the picture Discord already hosts. Both come from the same handshake with the Discord client on your PC that the id comes from, and they are stored so this site and the app can show which account is linked instead of a bare number. Nothing else about your Discord account is sent. Turn the pairing off in Settings and the rows are deleted, name and avatar included.
While you are in a match: the match id and the player ids of your own party, reported at agent select. That is what lets other players' apps show your group and yours show theirs. There is no switch for it, because the groupings only exist as long as every Valoranchi client in the match reports its own. Playing solo reports a party of one, which is never shown to anybody. Only your own group, only for that match, and deleted six hours later. No record is kept of who you play with.
Every match you finish, whether or not it's competitive: your agent, your kills, deaths and assists, your rank if it was ranked, and who was in your party. Unlike everything above, this one doesn't expire and has no switch. See "Match history" below for the honest version of that sentence.
Match history
Every match you finish, whether or not it's competitive, is reported by the app the moment it ends: which agent you played, your kills, deaths, assists and shot placement, your rank if it was a ranked match, and the puuids of whoever was in your party. This is the data behind Radiant Reputation, the Discord /stats command, and none of it (a peak, an act total, a ranking of who you queue with most) can be worked out from a single match. It needs a history.
Party sharing, above, also has no switch, but it expires in six hours. Match history doesn't expire at all: once a match is reported, it stays for as long as Valoranchi's database exists. That's a real difference in degree from everything else on this page, and it deserves saying plainly rather than being folded into a bullet next to the six-hour ones.
There's no button for this yet. If you want your match history deleted, write to legal@valoranchi.app and ask. It will be done by hand until there's a proper control for it in the app. Your Discord pairing is a separate, existing switch and is unaffected either way.
Whether someone else can trigger a lookup through Discord, by running /stats with your account chosen or by right-clicking you, is public by default, the same posture Tracker uses; see the bot page for how the two commands work. Turning it private is a toggle in Valoranchi's own Settings, not here, and it only changes who may ask: the retention above doesn't change either way, and your own /stats always works for you regardless of the setting.
What is never asked for
Your Riot password. The app has no screen that asks for it and no code that reads it. Signing in always happens in the Riot Client.
Your email, your ID, your payment method or any billing detail.
Discord
Discord activity (showing what you're playing) talks to the Discord app installed on your PC, locally. What Discord does with it is governed by your own privacy settings there.
The pairing between your Discord account and your Valorant account is made by the app, which is the only thing that sees both at once. It reports your Discord id, your display name and your avatar identifier, and nothing else. All three come from the handshake the Discord client on your PC already answers, so the app never asks Discord for anything about you and there is no extra permission for you to grant.
Deleting your data
Turn off the Discord pairing in Settings and no Discord row of yours remains on the server side. The match groupings work differently: there is no switch and nothing to delete by hand, since they expire on their own six hours after the match.
Uninstalling deliberately leaves your settings and loadouts on your disk, so reinstalling doesn't lose your saved accounts. They can be deleted by hand from the application's data folder.
Match history has no delete button yet. See "Match history" above for how to ask for it by hand.