You don’t need millions of observations by better than Hubble telescopes, our ancestors discovered 5 planets with their naked eyes.
Let’s assume we aren’t interested in iceballs like Pluto, or ice giants like Neptune and Uranus.
Here’s what you do. Travel FTL to the habitable zone of the star. Look for bright objects. If there is are planets near the habitable zone, they are likely to be as bright as Venus and Mars are from Earth. Venus is the third brightest object in Earth’s sky, after the Sun and Moon. If you see a really bright object you have a candidate planet. Zoom FTL perpendicular to that bright object an AU or so. Did it move against the fixed stars? You found a planet with your naked eyes.
And if you have a telescope–backyard hobbyist quality–you don’t need to move, you can just point your telescope at that bright object. Does it resolve into a disk? If so you’ve found a planet.
We don’t need to catalogue every planet in the system, not even every large planet, because we don’t care about planets above the boiling point of water or below the freezing point of carbon dioxide. You don’t need to check every faint spot of light for movement like astronomers did when they found the outer planets because we don’t care about the outer planets. When you’re in the inner system any inner system planet is going to be as bright as Mars or Venus and is going to show a disk through a hobbyist telescope and is going to change position against the stars every day.
And a small radio telescope could tell us if the native use radio. Any planet putting out lots of radio waves is very likely to be inhabited. Be careful of those ones.