You could turn on gamerule doTileDrops whenever the player is near that block.

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You could use /loot to give yourself the block, but that only works before it is mined:

loot give @s mine <coordinates>

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You could just simply /give the block to the player, if you already know what it is.

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You could /kill the drop whenever a different player is nearby.

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You could /clear the item out of other players' inventories.

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You could use spawn protection on a server and /op yourself so that you can still place and mine inside the spawn protection area.

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You could put other players into Adventure mode when they are nearby.

Yes

If you have a list of ores/other blocks you want this to work on use these 4 commands:

/scoreboard objectives add DiamondOre minecraft.mined:minecraft.diamond_ore

Then have a repeating command block with:

execute if score DiamondOre matches 1 run scoreboard players remove (YourNameHereI) DiamondOre 1

Then place a chain command block set to conditional with the line:

give (YourNameHere) diamond

Then you need to turn of tile drops using:

/gamerule doTileDrops false