I tried all the possible options in random.method, but I still got the same message -
Error in solve.default(vcov(x)[names.coefs_wo_int, names.coefs_wo_int], :
system is computationally singular: reciprocal condition number = 9.29205e-18
The reciprocal condition number changes for the different options.
However, when I log transformed one of the variables, the issue didn't occur.
Edited: Aug 20, 2022 - I think this is because of degrees of freedom issues and also STATA can model such a case but R's current package is unable to.