To talk about the periodicity of group 1 metals its important to know the chemicals involved and the theories that allowed these chemicals to be grouped.
One of the first group 1 metals discovered around the ancient times was sodium. However it was not associated with elements until much later on, rather it was known as a compound composed of chlorine and sodium to form salt. Alongside sodium, potassium was also discovered and used during the ancient times in the form of potash. Both these elements were however not considered fundamentally different until the 1700s when Georg Ernst Stahl had obtained evidence to suggest sodium and potassium were different and Henri-Louis Duhamel du Monceau was able to prove this difference in 1736.
In 1807 pure potassium was isolated using electrolysis (first time electrolysis isolated a metal) by Sir Humphry Davy and later that year sodium was also isolated using a similar technique thus demonstrating the two to be elements. Around the 1800s a new compound Petalite was discovered and in 1817 while analysing the petalite ore, Johan August Arfwedson detected the presence of a new element similar to sodium and potassium but not exactly the same as it had different properties. He named it lithium. Lithium, sodium and potassium became part of the discovery of periodicity by Johann Wolfgang Döbereiner in 1850 as they had similar properties which allowed them to be put into the same groups.
Döbereiner’s organisation of elements into triads came from lithium, sodium and potassium as they were all soft and reactive metals and when arranged by atomic weight, the second member of each triad was around the average of the first and third member. Soon many other scientists started to take the same approach using the law of triads and had organised relationships between various groups of metal. The problem was there was yet to be a complete table that included all the elements.
in 1869, Dmitiri Mendeleev published his version of the periodic table acquiring previous knowledge and by organising the elements in rows and columns in order of atomic weight and starting a new row when characteristics began to repeat. The reason Mendeleev received recognition of his table was because he was able to predict characteristics of elements he left gaps for as they were yet to be discovered. Soon with minor adjustments, his table became known as the common layout of the periodic table.

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Reference:
https://en.wikipedia.org/wiki/Alkali_metal https://en.wikipedia.org/wiki/Periodic_table#Periodic_trends_and_patterns https://www.britannica.com/science/alkali-metal