Observer design using observability staircase form

My original system (A, B, C, D) is observable, however, when I convert it to observability staircase form using obsvf function, the new system (Abar, Bbar, Cbar, Dbar) becomes observable.

A = [0,                     1,                          0;
    -807130.825379001,      -1372.23052244462,          0.0223832471519321;
    350984563219.344,       -417971392224.394,          -277869.165644330];
B = [0;
     0;
     276502.948306206];
C = [0,0,1];
D = 0;
Obsv_matrix = obsv(A,C);
if rank(Obsv_matrix) == size(A,1)
    disp('Original system is observable');
else
    disp('Original system is unobservable');
end   

Original system is unobservable

[Abar,Bbar,Cbar,T,k] = obsvf(A,B,C);
Dbar = D;
Obsv_new = obsv(Abar,Cbar);
if rank(Obsv_new,1e-10) == size(Abar,1)
    disp('Modified system is observable');
else
    disp('Modified system is unobservable');
end

Modified system is observable

My question is: if I design an observer gain Lbar for the new system using:

desired_poles = [-150-150*j, -150+150*j, -150];
Lbar = place(Abar',Cbar',desired_poles)'

Lbar = 3×1

1.0e+05 * 0.0000 -0.0000 -2.7879

is it possible to use the transformation matrix T to transform Lbar to find L that will be the observer gain for the original system? If not, what is the (intuitive) purpose of doing this transformation in the first place?

Thanks for your help in advance. Really appreciate any input.