What does the colon in µ-η2:η2-O2 mean?
This notation is mentioned in the IUPAC Nomenclature of Inorganic chemistry, Recommendations 2005 (‘Red Book’):


  IR-10.2.5.1 The eta (η) convention
  
  The special nature of the bonding of unsaturated hydrocarbons to metals via their π-electrons
  has led to the development of the ‘hapto’ nomenclature to designate unambiguously the
  unique bonding modes of the compounds so formed. (…) The Greek
  symbol η (eta) provides a topological description by indicating the connectivity between the
  ligand and the central atom. The number of contiguous atoms in the ligand coordinated to the
  metal is indicated by a right superscript numeral, e.g. η3 (‘eta three’ or ‘trihapto’), η4 (‘eta
  four’ or ‘tetrahapto’), η5 (‘eta five’ or ‘pentahapto’), etc.
  
  (…)
  
  If an unsaturated hydrocarbon serves as a bridging ligand, the prefix μ (see Sections
  IR-10.2.3.1 and IR-10.2.3.4) is combined with both η and κ, where necessary. The colon is
  used to separate the locants of the bridging ligand which indicate binding to different metal atoms.
  
  (…)
  
  Examples:
  
  21.
  
  
  
  (μ-η2:η2-but-2-yne)bis[(η5-cyclopentadienyl)nickel](Ni—Ni)


(This convention is not used for unsaturated hydrocarbons only, there is also a more complicated example (25) with carbonyl (CO) ligand.)

Use of this notation for formulae does not seem to be explicitly mentioned or “allowed”. If it is not an omission in the rules, I think that such construct could be called a name-formula hybrid, which might useful for detailed description the discussed structure detail in a shortest way possible.

The $\ce{[^{n}Bu4N]2[(UO2)2(\mu-\eta^2:\eta^2-O2)(NO3)2(\mu-Au(CN)2)2]}$ polymeric complex is described in [1], which talks about $\ce{U-O2-U}$ linkage with bidentate peroxo ($\ce{O2^{2-}}$) unit.

References:


Brown, M. L.; Ovens, J. S.; Leznoff, D. B. Dicyanoaurate-Based Heterobimetallic Uranyl Coordination Polymers. Dalton Transactions 2017, 46 (22), 7169–7180.