Block[{Print},<<xAct`xTras`];
$PrePrint=ScreenDollarIndices;
$CovDFormat="Prefix";
$DefInfoQ=False;
$UndefInfoQ=False;
$CommuteCovDsOnScalars=True;

DefManifold[Mr,1,{𝓍,𝓎,𝓏,𝓌}]
DefManifold[Mt,1,{s,u,v,p,q}]
DefManifold[M2,2,{𝒶 ,𝒷,𝒸,𝒹,ℯ,𝒻}]
DefManifold[M,{M2,Mr,Mt},{𝒜,ℬ,𝒞,ℰ,ℱ}]
SplitManifold[M, {M2,Mt,Mr}]

DefMetric[-1,G[-𝒜,-ℬ],Cd,SymbolOfCovD->{";","∇"}]
DefMetric[1,g[-𝒶,-𝒷],cd,SymbolOfCovD->{",","D"}]
DefMetric[1,fr[-𝓍,-𝓎],PD,FlatMetric->True,SymbolOfCovD->{",","∂"}]
DefMetric[1,ft[-s,-u],PD,ProtectNewSymbol:>$ProtectNewSymbols,FlatMetric->True,SymbolOfCovD->{",","d"}]

DefTensor[U[-𝒶],M2]
DefTensor[β[],M2]
DefTensor[V[],M2]
DefTensor[er[-𝓍],Mr]
DefTensor[et[-s],Mt]

er[𝓌]*et[p]*ft[-s,-u]*PD[-p][PD[-𝓌][V[]]]+er[𝓌]*ft[-s,-u]*U[𝒶]*V[]*PD[-𝒶][PD[-𝓌][β[]]]

I expect that the command “ToCanonical” does not do anything to the above expression. However, as shown in the next line,  it mixes different indices related to different submanifolds in an incorrect way.
WHY?

er[𝓌]*et[p]*ft[-s,-u]*PD[-p][PD[-𝓌][V[]]]+er[𝓌]*ft[-s,-u]*U[𝒶]*V[]*PD[-𝒶][PD[-𝓌][β[]]]//ToCanonical[#,UseMetricOnVBundle->None]&

And also, another a-bit-unexpected result!

er[𝓌]*et[p]*ft[-s,-u]*et[-p]er[-𝓌]V[]//ToCanonical[#,UseMetricOnVBundle->None]&