Presumably your touch light is just supposed to turn the bulb on and off, not dim it?
Some of the DAR made table lamps, which are just touch on/off and come with the bulb you show, are designed to take not only LED bulbs, but also filament/halogen bulbs up to 40W. Is such information on your lamp, or in its instructions by any chance?
I am thinking that the touch switch electronics may not be designed to operate such a low power bulb as you are now trying to use. I was going to suggest an LED bulb of 2.5w or 3w with a lower lumen output (ie a less efficient bulb) but I don't see any available lower than about 200 lumens.
Here is a possible, but not elegant, solution: If you can confirm your touch lamp base will operate filament bulbs up to 25W or 40W, then you could use a G9 to SES adapter, and then a 15W filament bulb, or choose a suitable alternative.
G9 To Small Edison Screw SES E14 Bulb Adaptor Lamp Socket Converter Holder - Ledlam Lighting - https://ledlam.lighting/accessories/adaptor-converters/g9-to-small-edison-screw-ses-e14-bulb-adaptor-lamp-socket-converter-holder/
Osram Oven Bulb | 15w E14 300Degree - https://www.lamps-on-line.com/osram-special-oven-lamp-240v-15w-e14-300-deg.html?gclid=EAIaIQobChMI14Hix-GP7gIVRJnVCh0reAbEEAQYBCABEgLlu_D_BwE
But only do this if you can confirm the touch switch is happy to operate a higher wattage (filament) bulb.