Is it considered a sin to delay the Fajr prayer until 1:0 PM due to janabah and the inability to perform ghusl on time, and was it permissible to perform tayammum to pray it?

A person in a state of major ritual impurity (junub) must perform ghusl (ritual bath) to perform the obligatory prayer when its time enters, because purity is a condition for the validity of prayer. If ghusl is not possible due to extreme cold, lack of water, or inability to use it, then tayammum (dry ablution) becomes obligatory, and the prayer must be performed within its prescribed time, as Allah Almighty says: "And if you do not find water, then perform tayammum with clean earth." Delaying prayer beyond its prescribed time due to major ritual impurity is a mistake, as it must be performed within its time, either with ritual purity or with tayammum if one is unable to use water.