No

Every class proficient with martial weapons is also proficient with simple weapons, so there would be no mechanical advantage to using a trident over a spear (unless in some unforeseen circumstance you needed the extra 1lb).¹

There would be a reason to use a spear (simple weapon) and not a trident (martial weapon), but not the other way around. Bards, clerics, druids, monks, rogues, and warlocks are proficient with simple weapons but not martial weapons. For them, their proficiency bonus would be an advantage of the spear over the trident.

However, these are not the only weapons with the same mechanics (other than price and weight). The following martial weapons are mechanically identical:

• battleaxes and longswords are both versatile weapons causing 1d8 (1d10 two-handed) slashing damage
• morningstars and war picks both cause 1d8 piercing damage

1. The "Variant Entertainer: Gladiator" background (PHB, p. 131) allows a player to "replace the musical instrument in your equipment package with an inexpensive but unusual weapon, such as a trident or net." RAW this only gives the trident as equipment. However, a DM could house rule that it also grants proficiency (in place of the music instrument from the Entertainer background). If allowed and taken by a sorcerer or wizard, they would have proficiency with tridents but not simple weapons (i.e, spears).

This is not balanced.

Okay, I don't usually do "is this balanced" questions, because I don't really know what 'balanced' is. But, to paraphrase Potter Stewart, "I know it when I see it, and this ain't it."

You've obviously tried to balance it, and that's laudable. And there may be room to make this concept balanced. But it's not there yet.

1. First-off, let's note that it's piecewise-equal to each of the weapons it's based off of. That is, in "dagger mode" it's as good as normal daggers, in "spear mode" it's as good as a normal spear, &c. for quarterstaff and javelin and the club-and-dagger variant.¹ This hits configurations 1 and 3-6.

   Then we get to configuration 2: I don't know what-exactly this is, but it does the damage of either a Greataxe or Greatsword while being half the weight of each and bearing the keywords Finesse and (!) Versatile, rather than the Heavy and Two-handed of the Great weapons. That extra ! is in there because it'd be the only Finesse and Versatile weapon other than sun blade, a rare.²

   [Thanks to SirTechSpec] Configuration #2 also gets into murky water with your druid's weapon proficiencies; a druid's got scimitars but not other swords, and this configuration looks a lot more like a sword or even a polearm than it does a scimitar.

   [Thanks to Eric] Another easily-overlooked problem is that your gnome is not capable of handling heavy weapons; you've created a non-heavy weapon that does the same damage as heavy weapons, so you've undercut this bit of racial balancing that the designers built in.

   So you've got something that's equal to existing weapons in five configurations, and is superior in all ways to two other existing ones in the sixth. At it's core, this design is unbalanced.

2. I see you tried to balance it through the action economy. Unfortunately, you didn't. Compare your tinkerer using this to someone carrying the five comparable weapons. (I'm ignoring configuration 2.) Your gnome has to spend an action (or less) to switch weapons.

   But our comparison-character would have to burn an action to achieve the same thing: stowing one weapon might be one of the "free" actions tabulated on PHB190, but "Use an Object" (PHB193) would come into play when drawing the second.

3. Weight: your whole thing weighs in at 4lb., I believe? Someone carrying all the implied weapons weighs in at 12lb. (I called your staff-sword a longsword, for weight purposes.)

4. I suppose some might argue that you can be disarmed of five weapons at once, which is the one drawback I can see of the whole design. But I think it's a hard row to hoe, calling that drawback equal to shedding 8lb. and gaining a Versatile, Finesse, one-handed, non-heavy Great[sword|axe].

There's another important way in which this isn't balanced.

All of the above addresses "in-game" balance: how will this character's capabilities compare to those of other characters. But I'd actually be more concerned about "table-balance." You've chosen to play a gnome, which has as one of its bits that you can design a little trinket, which probably doesn't come into play very often. But you're trying to bring that to an item that you're like to use during every round of combat.

To the extent that I can see combats at your table including any time spent on your character swapping configurations or you [the player] discussing with your table-mates which configuration would be best in this fight, you're unbalancing the table. You're creating a "weapon-picking" game that only you get to play, and it comes at the expense of your mates.

Wizards, particularly, and spellcasters, generally, also have to juggle this: they've often got many more options than martial characters. But their classes are build with forty years' experience balancing this. You're proposing a character have unique equipment with all this complexity, but no drawback. It's jut not really "playing nice" with your table.

^{1 - And I have to note here, I really like that bit distinguishing the javelin-mode and the spear-mode. You've done some nice fantasy-tinkerer-engineering here. Let nothing I say above detract from the interesting ideas and obvious thought you've put into this!}

^{2 - a wise (mini)man once told me that options=power. Versatile + finesse is giving lots of options, compared to other weapons.}