Wiring – different wiring in newly purchased ceiling fixture

Absolutely do not leave the wires alone wrapped in electrical tape. Electrical tape does not have enough longevity to safely protect the exposed leads and can create a hazard in the future.

The blue wire exists to support the future addition of a light. The polite thing to do for your future self or future owner of your home would be to connect the blue and red wires. However, it is not necessary; if you do not want to, you can cap both leads with wire nuts.

Note that it is also legitimate to connect the black on the fan to the red from the ceiling, and the blue on the fan to the black from the ceiling. Assuming you have two switches, that will swap which switch controls the fan and which switch controls the light.

If the existing black-black connection doesn't work, you can try the black-red. If that does work, it would suggest that the switch for the fan has failed, although it could also indicate other wiring problems.

The silver wire is also a ground. Chains are not grounding paths so a pendant needs 2 grounds - one down the chain to the pendant, and the other for the box cover.

I suspect the manufacturer ran an extra run of 14/2 (12/2?) Romex from the switch to support a ceiling fan which you don't have (yet). I bet the third black is folded up in the back of the box, but they tied this pair's white wire with the other white wires. That's making my spider-sense tingle, but I can't say why. Might make a good question.

Since the power is fed from the switch (no weird switch loops) you should be able to connect all blacks to each other, ditto the whites. All grounds must be connected together. I don't see any obvious way that upper steel plate bonds to the maze of ground wires above it, and that makes me a bit nervous. Is that a steel box above, and is the ground bundle bonded to it in some way? I see a screw, but it's not green and may be a physical mounting. Is the steel cover plate tightly screwed to the steel box?

As far as wire-nuts, each make of wire-nut is listed for certain combinations of wire. For instance Ideal's 73B (orange), 74B (yellow) and 76B (red) are covered in a document titled UL Listed wire combinations... Generally I like to be in the middle of the working range for a wire-nut, so I'd go yellow for 3 wires, red for 4, and orange for something that seemed on the smallish range for yellow.