You define a friendly URL, load the page, and the address reads /discord/discord/invite/abc123. The route works, nothing errors, and the duplication looks like a typo somewhere you cannot find.

It is not a typo. Invision Community prepends topLevel to every friendly path in the file. Repeat it in the path and you get it twice.

Wrong

{
    "topLevel": "discord",
    "pages": {
        "myapp_invite": {
            "friendly": "discord/invite/{@key}",
            "real": "app=myapp&module=discord&controller=invite"
        }
    }
}

Produces /discord/discord/invite/abc123.

Right

{
    "topLevel": "discord",
    "pages": {
        "myapp_invite": {
            "friendly": "invite/{@key}",
            "real": "app=myapp&module=discord&controller=invite"
        }
    }
}

Produces /discord/invite/abc123.

The top-level landing page is the exception, and it is an empty string

The obvious guess for "the page at /podcasts" is "friendly": "podcasts". That gives you /podcasts/podcasts/. Every core application uses an empty string instead:

grep -A2 '"topLevel"' applications/forums/data/furl.json
#   "topLevel": "forums",
#   "pages": { "forums": { "friendly": "", ... } }

So:

{
    "topLevel": "podcasts",
    "pages": {
        "myapp_index":   { "friendly": "",                "real": "..." },
        "myapp_show":    { "friendly": "{#id}-{?}",       "real": "..." },
        "myapp_episode": { "friendly": "episode/{#id}-{?}","real": "..." }
    }
}

Which gives /podcasts/, /podcasts/12-my-show/ and /podcasts/episode/34-my-episode/.

The placeholder types are not interchangeable

A second way to lose an afternoon. {#name} is a number and {@name} is a string:

"friendly": "invite/{#key}"   <-- a hex key becomes 0. Every link resolves to the same record.
"friendly": "invite/{@key}"   <-- correct for anything non-numeric

Use {?} for a slug you do not intend to read back — the human-readable part of /podcasts/12-my-show/.

Check it rather than assume it

Neither mistake throws. Both produce URLs that resolve, so tests pass and the page loads. Print the URLs once, from code, and read them:

printf( "%s\n", Url::internal(
    'app=myapp&module=x&controller=y&id=1', 'front', 'myapp_show', array( 'the-slug' )
) );

This matters more than tidiness for anything a person keeps. A podcast feed address is permanent once somebody subscribes; an invite link gets pasted into chat and printed on things. Fixing the URL later means breaking every copy of it that already exists.

Related: A Pages category created in code sends every article into a redirect loop, The core/ContentRouter extension in Invision Community 5

Related application: Podcasts — Podcasts gives each show a readable, permanent feed address like /podcasts/feed/12-my-show, because that URL cannot be tidied up once anybody has subscribed to it.