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I use QGIS 3.22.2 and I have points datasets of records from ecology surveys with column of "ID" of individual record and column "Species" with few different values (for example: 'Pip', 'Pop', 'Pep' and 'Pap') and I need to make rule based symbology with different symbols for different "Species", almost all of records from same species will have same offset points (0,0), but to avoid points overlapping I need for some records of same "Species" - for example: "Species"='Pip' - with given particular "ID" - for example "ID"='2' I would like to have offset points set up on (3,4) and for "ID"='5' I would like to have offset points set up on (5,6), etc.

How and where I can set up this kind of Rule-based symbology in QGIS?

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You can use the data defined override of the symbol offset x and y with an expression, like so:

enter image description here

Expression
case 
    when $id = 2 then '3,4'
    when $id = 5 then '5,6'
    --else '7,8' -- you can also use `else` in a `case` statement (delete the leading -- to uncomment)
end

If you don't use else in the above statement, the ids not caught by the expression (everything other than 2 and 5) will be unaffected (0,0 offset).

Result

enter image description here

I use the Meters at scale measurement unit for some extra distance in my screenshot

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