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Maybe we should look off planet, look to the Lagrange points: https://en.wikipedia.org/wiki/Lagrange_point

We might find some old equipment from an elder spacefaring species. If we don't find anything, maybe we should leave some human monuments out there so the next civilization can know about us.

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As the Wikipedia article mentions, we’ve already done just this with the JWST…

Naw the JWST won't stay there after it loses power.

> The points L1, L2, and L3 are positions of unstable equilibrium. Any object orbiting at L1, L2, or L3 will tend to fall out of orbit; it is therefore rare to find natural objects there, and spacecraft inhabiting these areas must employ a small but critical amount of station keeping in order to maintain their position.

Nothing will. The Lagrange points are only quasi stable.

L4 and L5 are "stable" -- but of course on timescales of billions of years even Earth's orbit isn't guaranteed to be stable.

Lagrange Point orbits still require station-keeping. Anything 'parked' there will eventually float away from it, unless the position is actively maintained.

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