This is what we found on Wikipedia regarding the Bahrain Summer Toy Festival at Exhibition World Bahrain:

Formula One sponsorship liveries have been used since the 1968 season. Before the arrival of sponsorship liveries in 1968, the nationality of the team determined the colour of a car entered by the team, e.g. cars entered by Italian teams were rosso corsa red, cars entered by French teams were bleu de France blue, and cars entered by British teams (with several exceptions, such as cars entered by teams Rob Walker, Brabham, and McLaren) were British racing green. Major sponsors such as BP, Shell, and Firestone had pulled out of the sport ahead of this season, prompting the Fédération Internationale de l'Automobile to allow unrestricted sponsorship.

Team Gunston became the first Formula One team to implement sponsorship brands as a livery on their Brabham car, which privately entered for John Love in orange, brown and gold colours of Gunston cigarettes in the first race of the 1968 season, the 1968 South African Grand Prix, on 1 January, 1968. In the next race, the 1968 Spanish Grand Prix, Team Lotus, initially using British racing green, became the first works team to follow this example, with Graham Hill's Lotus 49B entered in the red, gold and white colors of Imperial Tobacco's Gold Leaf brand. With rising costs in Formula One, sponsors became more important and thus liveries reflected the teams' sponsors.

Tobacco advertising was common in motorsport for decades; as bans spread throughout the world during the late 20th and early 21st century, teams began using an alternate livery which alluded to the tobacco sponsor. At historical events, cars are allowed to use the livery which was used when the car was actively competing. Prior to 2022, special liveries were uncommon; excluding country-specific legislation that would require mandatory changes to specific sponsorship elements, most commonly tobacco and nicotine, very few one-off liveries were run in Formula One. The Jaguar team introduced their first one-off livery at the 2004 Monaco Grand Prix, beginning a trend of one-off liveries that continued until the early 2010's. Since then, special liveries were uncommonly seen on track. In 2021, a special livery introduced by McLaren for the Monaco Grand Prix required them to receive special dispensation from the FIA. Since then, the amount of special liveries run by teams on the grid have increased.