It seems the tiedscalar magic is somehow being applied incorrectly, when a 'virgin' readonly scalar is being used in a bitwise OR operation. With 'virgin' I mean that the variable hasn't been accessed before. Once the variable has been accessed/initialised (note the difference in the Devel::Peek dump before and after), things start to work as expected, i.e. the OR operation then seems to default to numeric interpretation. Compare:

use Devel::Peek;
use Readonly;

Readonly my $C1 => 0x0004;
Readonly my $C2 => 0x0008;
                         
Dump($C1);           # before first evaluation
#Dump($C2);

my @x = ($C1, $C2);  # somehow access variables

my $C3 = $C1 | $C2;

Dump($C1);           # after first evaluation
#Dump($C2);

print "\nValue of C3 = ", $C3, "\n";
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If you comment out the line "my @x = ($C1, $C2);", $C3 will be "<" (i.e. string OR of "8" | "4"), while with the line being active, you'd get 12 (i.e. numeric OR of 8 | 4 ).

Example output without pre-evaluating $C1 and $C2:

SV = PVMG(0x69b788) at 0x65eb00
  REFCNT = 1
  FLAGS = (PADBUSY,PADMY,GMG,SMG,RMG)
  IV = 0
  NV = 0
  PV = 0
  MAGIC = 0x6e8ff0
    MG_VIRTUAL = &PL_vtbl_packelem
    MG_TYPE = PERL_MAGIC_tiedscalar(q)
    MG_FLAGS = 0x02
      REFCOUNTED
    MG_OBJ = 0x63c430
    SV = RV(0x676bd8) at 0x63c430
      REFCNT = 1
      FLAGS = (ROK)
      RV = 0x6b87d0
      SV = PVMG(0x69b750) at 0x6b87d0
        REFCNT = 1
        FLAGS = (PADBUSY,PADMY,OBJECT,IOK,POK,pIOK,pPOK)
        IV = 4
        NV = 0
        PV = 0x7083b0 "4"\0
        CUR = 1
        LEN = 8
        STASH = 0x6b8990        "Readonly::Scalar"
SV = PVMG(0x69b788) at 0x65eb00
  REFCNT = 1
  FLAGS = (PADBUSY,PADMY,GMG,SMG,RMG,pIOK,pPOK)    # <---
  IV = 4
  NV = 0
  PV = 0x6b4c50 "4"\0
  CUR = 1
  LEN = 8
  MAGIC = 0x6e8ff0
    MG_VIRTUAL = &PL_vtbl_packelem
    MG_TYPE = PERL_MAGIC_tiedscalar(q)
    MG_FLAGS = 0x02
      REFCOUNTED
    MG_OBJ = 0x63c430
    SV = RV(0x676bd8) at 0x63c430
      REFCNT = 1
      FLAGS = (ROK)
      RV = 0x6b87d0
      SV = PVMG(0x69b750) at 0x6b87d0
        REFCNT = 1
        FLAGS = (PADBUSY,PADMY,OBJECT,IOK,POK,pIOK,pPOK)
        IV = 4
        NV = 0
        PV = 0x7083b0 "4"\0
        CUR = 1
        LEN = 8
        STASH = 0x6b8990        "Readonly::Scalar"

Value of C3 = <
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Strange...