Cut fennel bulb lengthwise into 1/4-in.-thick slices. Put into a medium bowl, cover with water, and chill at least 30 minutes and up to 1 day.
Make the tapenade: Put tuna, parsley, anchovies, capers, and thyme in a food processor and whirl until mixture turns into a smooth paste, pausing often to scrape sides with a spatula. Add olives and mustard and whirl until smooth. With food processor running, slowly pour olive oil into top. Turn tapenade out into a serving bowl.
Set a steamer basket in a large pot and fill pot with enough water to come just below basket. Cover and bring water to a boil over medium-high heat. Add beans, cover, and steam until tender-crisp, 4 to 5 minutes. Transfer to a bowl and let cool. Steam cauliflower next, transferring to another bowl when just losing its crispness, about 2 minutes. Add more water to pot if necessary and steam potatoes until tender when pricked with tip of a sharp knife, 15 to 20 minutes; transfer to a bowl and set aside. Let cool till just warm or, if serving later, cover and chill.
Drain fennel and arrange on a platter with radishes, tomatoes, and steamed vegetables; serve with tapenade.
Note: Nutritional analysis is per 1/4 cup.